The theorists at APC have a very broad range of interests. Their research is both closely linked with observations and focussed on fundamental theories. This activity addresses crucial open issues in astroparticle physics, cosmology, quantum field theory, gravity and string theory and is at the forefront of this research. The main subjects of the APC theory group are:

**Themes**

**Gravity**

**General relativity and modified gravity theories** [N. Deruelle, E. Kiritsis, D. Langlois, J. Mourad, D. Steer]

The study of possible deformations of general relativity is of major theoretical and phenomenological importance, and is an area in which a number of people in the theory group are actively working. A number of questions can be addressed. Firstly, from a theoretical point of view, it is possible to modify General Relativity in a mathematically consistent way (free of instabilities and ghosts, etc) ? If so, can these theories be experimentally viable, that is consistent with GR at least on scales ranging from ~1mm to solar system ? And finally might they provide an a alternative, and hopefully more natural, explanation for the observed late time acceleration of the universe today ?

In recent years, members of the group have worked on several theories of modified gravity. These include f(R) and chameleon theories, in which we have studied for instance at the structures of stars as well as spherical collapse. A lot of work has been done on the so-called Galileon models, which we have generalised as well as covariantised. Finally, a number of members of the group are working intensively on the (in principle) ghost-free formulation of massive gravity, its cosmological solutions, and the Vainshtein mechanism.

The dynamics and problems of massive gravity are also investigated by using the holographic link to Quantum Field Theory. This same link makes massive gravity a model for studying momentum dissipation in finite density strongly coupled systems with potential applications to condensed matter physics.

**Gravitational waves** [P. Binetruy, C. Caprini, N. Deruelle, D. Steer]

The year 2016 has witnessed two experimental milestones in the quest for detecting gravitational waves (GWs) from Earth and from space: the first direct detection of a GW signal by the two Earth-based interferometers LIGO, and the demonstration by the LISA Pathfinder satellite of the technology needed for detecting GWs from space. GWs direct detection opens a new window on the universe, marking the beginning of the GW astronomy era. Through their GW emission, it is possible to detect objects that are invisible via electromagnetic radiation, providing access to formerly unknown populations of sources. Moreover, due to the weakness of the gravitational interaction, GWs propagate freely through the universe carrying direct information about its status up to epochs never observed before: both Earth-based and space-based interferometers have in principle access to a stochastic gravitational wave background formed in the very early universe, long before it became transparent to photons. Therefore GW detection provides us with a unique opportunity to test the universe via a new messenger, fully complementary to electromagnetic radiation. In the APC theory group we explore this opportunity, in particular concerning the potential of the LISA mission, ESA space-based laser interferometer, to probe cosmology. We coordinate the work within the Cosmology Working Group of the LISA Consortium.

**Gravitational waves from the early Universe **[P. Binetruy, C. Caprini, N. Deruelle, D. Steer]

A stochastic GW background can arise from high-energy processes in the very early universe: typically from inflation, from phase transitions, from topological defects, from primordial black holes. The detection of such a cosmological background would be revolutionary, as it would bring information on the physical theory describing the status of the primordial universe, making it possible to also falsify models. It can be considered as the ultimate pay-off of GW experiments. We are actively involved in studying different primordial sources of GWs: cosmic strings and superstrings, inflation and preheating, and primordial phase transitions. In the case of cosmic strings, we have revisited and improved previous computations, and particularly studied if such sources could be observable by LIGO/VIRGO and LISA. In the case of GWs emitted by cosmic superstrings networks, we have also determined for the first time the effects of 3-way junctions, typical of such networks. Concerning the GW emission by first order phase transition, we develop analytical methods to model the shape of the GW energy density power spectrum from bubble collisions, sound waves and magnetohydrodynamic turbulence in the primordial plasma. However, the detection of a stochastic GW background is technically extremely challenging: because of its intrinsic nature, distinguishing it from the detector noise requires a high level of sophistication in the data analysis process. In collaboration with members of the Gravitation group, we develop techniques to assess the capability of LISA to detect a stochastic background.

**Gravitational waves and the expansion of the universe **[C. Caprini]

The LISA mission can detect the GW signal from inspiralling and merging black hole binaries up to very high redshift. After emission, GWs propagate freely through the Universe, which can be used as a probe of the Universe expansion and spacetime characteristics. The detection of a GW signal provides a very clean measurement of the luminosity distance of the GW source. If a determination of the source redshift is available, either by coincident detection of an electromagnetic counterpart, or directly in the gravitational waveform by non-standard terms breaking the degeneracy between redshift and chirp mass, the GW signal can be used to test the distance-redshift relation and infer the cosmological parameters. Moreover, GWs propagate from the source to the detector through the cosmological matter structure: traces of this propagation through the perturbed spacetime can be detectable in the gravitational waveform, and could also be used in the future to test cosmological parameters. In the theory group of APC we study these subjects from a theoretical point of view as well as their application to the LISA mission.

**Astroparticles**

**Neutrino physics and astrophysics **[D. Semikoz, C. Volpe]

Neutrinos tell us stories from sources far away in space and time. After the discovery of neutrino oscillations, an impressive progress has been made in our knowledge of neutrino properties in the past decade. Still, they remain intriguing elementary particles that still have key unknown properties to reveal. These include their absolute mass and mass ordering, leptonic CP violation, the neutrino Majorana or Dirac nature and the existence of a fourth sterile neutrino. Their measurement will bring fundamental bricks for physics beyond the Standard Model of particles and interactions. Neutrinos are also intimately connected with major astrophysics questions, of the energy production in stars, of the end of life of massive stars and of the origin of the elements that make up stars and our Universe. In particular, uncovering how neutrinos change flavor in such environments is essential for these issues. The cold background of cosmological neutrinos is yet to be discovered, while it has left an imprint on the nucleosynthesis of light elements (big-bang nucleosynthesis) and on large scale structures. The APC theory group works at the forefront of this research, investigating fundamental aspects, conceiving new avenues, or in close connection with experiments.

**Neutrino flavor evolution in astrophysical environments** [C. Volpe]

Important progress is ongoing in our understanding of how neutrinos change flavor in astrophysical environments, in particular core-collapse supernovae. In fact, neutrinos change flavor in unexpected ways in massive stars, compared to the case of our Sun. It is now established that the solar neutrino deficit is due to the Mikheev-Smirnov-Wolfenstein effect - a resonant adiabatic flavor conversion phenomenon due to the neutrino interaction with matter. In massive stars, novel neutrino conversion phenomena are being uncovered due to the presence of the neutrino interaction with neutrinos and to dynamical aspects related to the star explosion - shock waves and turbulence. While many features are now understood important open questions need to be addresses in the future. Theoretically, various methods can be employed for the description of neutrino propagation in astrophysical and cosmological environments, going across domains, such as systems of spins moving in effective magnetic fields, algebraic methods, or many-body approaches known in the study of atomic nuclei, of clusters or of condensed matter. Phenomenologically these studies are essential, to put on a solid ground, predictions of neutrino supernova signals associated with an (extra)galactic explosion, or of the diffuse supernova neutrino background yet to be discovered, or to assess the impact on the supernova dynamics and stellar nucleosynthesis.

**UHE neutrinos** [D. Semikoz]

Ultra-High Energy (UHE) cosmic rays produce secondary charge pions on background fields in the sources or in intergalactic space. Neutrinos produced during propagation are called "cosmogenic neutrinos". Flux of those neutrinos depends on the unknown distribution of sources and on the initial proton spectrum produced at those sources. Experiments like ANITA, AUGER and ICECUBE will be able to study this flux. For direct neutrino flux from the sources even backgrounds are unknown or at least model dependent. This make predictions of neutrino flux from sources even more difficult. We are developing theoretical models of UHE neutrino sources.

**Cosmological neutrinos at the epoch of big-bang nucleosynthesis** (D. Semikoz, C. Volpe)

Big Bang Nucleosynthesis (BBN) is one of key stones of cosmology. When the Universe cools down to sub-MeV temperatures, the plasma is not hot enough anymore to destroy light nuclei, produced from protons and remaining neutrons. The abundances of light elements is then governed by the neutron-to-proton ratio, which in turn depends on reactions with electron neutrinos and anti-neutrinos as well as neutron decay, and on the total energy density of Universe at that time. The observed abundances of light elements strongly restrict any new physics connected with MeV scales. This offers a poweful tool to constrain the parameter spaces of exotic models or novel particles such as sterile neutrinos.

**Low energy weak interaction and neutrino physics** (C. Volpe)

Low energy weak interaction and neutrino physics has brought milestone in the build up of the Standard Model. Nowadays it is a powerful tool to search for new physics beyond it. The group has been strongly contributing to this domain by predicting neutrino-nucleus cross sections crucial for the interpretation of oscillation experiments, exploring the connection with the lepton-flavor violating neutrinoless doble-beta decay, proposing experiments nearby existing facilities such as spallation source ones (ESS), investigating other low energy weak processes. The group is also renown for the proposal of a novel neutrino facility in the 100 MeV energy range based on a new concept : the low energy beta-beam. This facility is of great interest for nuclear physics, neutrino and supernova physics.

**Cosmic Rays **[D. Semikoz]

Cosmic rays with energies E > 1018 eV (or 1 EeV) called Ultra High Energy Cosmic Rays (UHECR). The UHECR proton spectrum is strongly suppressed above E > 5 x 1019 eV due to pion production on cosmic microwave photons, the so called Greisen-Zatsepin-Kuzmin (GZK) cutoff. Such suppression was found by HiRes experiment and Pierre Auger Observatory. We study theoretical models for spectrum, composition and sources of UHECR, propagation of UHECR in the intergalactic medium. We are collaborating with APC group of JEM-EUSO project.

**Gamma-Ray Astrophysics** (D. Semikoz)

There are two classes of observations, which connect gamma-ray astrophysics and UHECR. First, sources of TeV gamma-rays can in principle accelerate cosmic rays to ultra-high energy. Then observed TeV gamma-rays can be partly produced in the UHECR acceleration mechanizm or due to cosmic ray energy losses in the sources. Second, diffuse gamma-ray background at GeV energies observed by Fermi satellite contain fraction due to UHECR energy losses. How large is this fraction depends on distribution of UHECR sources and evolution of their luminosity. We study secondary GeV-TeV gamma-rays in variety of models.

**Cosmology**

**Inflation and cosmological perturbations **[P. Binetruy, N. Deruelle, E. Kiritsis, D. Langlois, D. Steer]

Cosmological observations, in particular the CMB anisotropies, point to the existence of primordial fluctuations, with a spectrum close to but distinct from scale-invariance. The best current explanation for the origin of these fluctuations is a phase of accelerated expansion, called inflation, in the early universe. This scenario was proposed more than 30 years ago and has survived the tremendous improvement of observations. The nature of the inflaton field, however, is still an open question. In recent years, several members of the group have worked on various models of inflation, in particular those involving several scalar fields, and studied their detailed signatures, which are potentially detectable in present or future data. Important specific signatures include non-Gaussianities and isocurvature perturbations.

The process of cosmological inflation is technically similar to approximate conformal invariance and scaling in Quantum Field Theory. This analogy is made precise by the gauge/gravity duality and it points to a completely different view of the standard problems of inflation. This QFT/inflation link is currently under scrutiny.

**Cosmological neutrinos at the epoch of big-bang nucleosynthesis ** [D. Semikoz, C. Volpe]

Big Bang Nucleosynthesis (BBN) is one of key stones of cosmology. When the Universe cools down to sub-MeV temperatures, the plasma is not hot enough anymore to destroy light nuclei, produced from protons and remaining neutrons. The abundances of light elements is then governed by the neutron-to-proton ratio, which in turn depends on reactions with electron neutrinos and anti-neutrinos as well as neutron decay, and on the total energy density of Universe at that time. The observed abundances of light elements strongly restrict any new physics connected with MeV scales. This offers a poweful tool to constrain the parameter spaces of exotic models or novel particles such as sterile neutrinos.

**Primordial magnetic fields **[C. Caprini]

Magnetic fields are observed in matter structures over a wide range of length-scales and redshift, and a lower bound on the intensity of the magnetic field in voids has also been established using data from gamma-ray telescopes. Finding an explanation for the ubiquitous magnetic fields in the universe is very challenging: the origin of the observed magnetic fields remains to date an open problem. One of the possible explanations that have been proposed is that they have been generated in the very early universe, either during inflation or during a primordial phase transition. We work on generation mechanisms operating in the early universe capable of explaining the magnetic field amplitudes observed today, as well as on theoretical and observational constraints that allows us to test the primordial hypothesis, such as the effect of primordial magnetic fields in the Cosmic Microwave Background temperature anisotropies and polarisation. In collaboration with members of the High Energy Astrophysics group, we study the lower bound on the magnetic field intensity in voids that have been established by gamma-ray telescopes and its application to primordial magnetic fields.

**Topological Defects **[N. Deruelle, D. Steer]

In the last years, members of the group have been behind important developments in the understanding of the dynamics of string and super-string networks with junctions. Cosmic strings can also have signatures other than Gravitational Waves, and in particular they can emit photons of different frequencies. Recently we have shown that kinks on current carrying cosmic strings emit transient radio bursts with characteristics (amplitude, duration and rate) very similar to the rare, cosmological, transient bursts recently observed by the Parkes telescope. This new observational signature may lead to important constraints on (or perhaps even the detection of!) current carrying cosmic strings.

**Quantum Field Theory, String Theory and interfaces**

**Quantum Field Theory in curved spacetime **[E. Hughet, E. Kiritsis, J. Renaud, J. Serreau]

The study of quantum effects in strong gravitational backgrounds is a subject of topical interest in cosmology and astrophysics. Paradigm examples are the gravitational amplification of primordial density perturbations in inflationary cosmology or the Unruh-Hawking radiation from black holes which are cornerstones of modern cosmology and of the fundamental understanding of black hole physics. More generally, understanding situations where both quantum and gravitational effects come into play sheds a new light onto the laws of physics at work and may give some insight concerning more fundamental laws.

**The Theory group of APC studies various aspects of this general question:**

**Conformal methods for fields in curved geometries** (E. Hughet, J. Renaud)

The general framework is that of quantization and more specifically quantum field theory on manifolds. After a period mostly devoted to the study of conformal scalar and Maxwell fields in de Sitter space, we are now considering fields in Robertson Walker spaces. Most of the works concerning this topic fails to give practical methods or uses flat space approximation methods. A motivation of the group is to obtain both exact and explicit expressions for objects - such as two-point functions - allowing for practical calculations and interpretations in quantum (and classical) field theory in curved backgrounds.

In this respect, we have developed, using the methods of differential geometry a formalism, which can be viewed as a generalization of the Dirac's six-cone formalism. In this formalism the conformally flat spacetimes are obtained as the intersection of the null cone of R6 and an hypersurface. In this context the Maxwell equations in a conformal gauge are converted to a set of conformal scalar equations. The application of this formalism is now in progress. These works lead us to generalize the use of the conformal transformations to non conformally-invariant equations.

**Interacting fields in de Sitter space** (J. Serreau)

The study of interacting scalar fields in de Sitter space is of notorious difficulty. The case of light fields in units of the inverse curvature, for which gravitational effects play a crucial role, is of particular interest, both theoretically and phenomenologically (e.g. for inflation). In that case, perturbative techniques are plagued by divergent contributions coming from low (physical) momenta or, equivalently, due to the gravitational redshift, late times. Such infrared/secular divergence signal important physical effects and must be resummed in order to get reliable answers. The group is active in developing resummation methods in de Sitter space and in applying them to questions of physical interest, e.g. in the context of inflationary physics. Examples of such methods include the p-representation of correlators, large-N techniques, 2PI techniques borrowed from nonequilibrium quantum field theory, or renormalization group techniques. Recent original results are, for example, the observation that due to nonperturbative infrared effects, quantum contributions to nonGaussian correlators of a light test scalar field contribute the same order of magnitude in the coupling constant as the tree-level contribution, or the fact that gravitationally amplified quantum fluctuations in the regime of infrared momenta systematically lead to the radiative restoration of spontaneously broken symmetries in O(N) theories in any space-time dimensions.

**Using Curved geometry as an IR regulator in gravitational and string theories ** (E. Kiritsis)

Gravitational quantum corrections apart from their well-known UV infinities have also serious IR infinities. Although some of these can be studied using dimensional regularisation, the same cannot be said about power IR divergences. The problem is therefore how to regulate the IR (and UV), keep power corrections, and preserve the diffeomorphism invariance.

The only known approach so far in this direction was developed by members of the group and collaborators. It uses an appropriate curved space-time background that induces a finite mass gap in the theory, regulating therefore the IR while maintaining background covariance. The UV divergences are regulated by embedding the theory in a string theory (that has the string scale as an effective UV cutoff). This approach has been developed over the years and is used currently to address problems in theories with softly broken diffeomorphism invariance, like massive graviton theories.

**Integral quantization of geometries **[J.P. Gazeau]

Integral quantization, which should be distinguished from path integral quantization (essentially based on canonical quantization), offers many ways to give a classical object a quantum version. It is a quantization of various geometries (like symplectic manifolds) which is based on operator-valued measures (POVM). We particularly insist on the probabilistic aspects appearing at each stage of the procedure. The so-called Berezin or Klauder or yet Toeplitz quantization, or coherent state quantization, are particular (and mostly manageable) cases of this approach.

The integral quantizations include of course the ones based on the Weyl-Heisenberg group (WH), like Weyl-Wigner and (standard) coherent states quantizations. It is well established that the WH group underlies the canonical commutation rule, a paradigm of quantum physics. Actually, we show that there is a world of quantizations that yield this rule. In addition, we enlarge the set of objects to be quantized in order to include singular functions (like angle or phase) or distributions (like Dirac and its derivatives). One of the interesting aspects of the integral quantization scheme is to analyze the quantization issues, particularly the spectral properties of obtained operators from functional properties of their symbols, through a kind of Berezin-Segal transform. Another appealing aspect of the above approach lies in its capability to quantize constraints.

Our approach also includes a less familiar quantization based on the affine group of the real line. The procedure is here based on affine coherent states or wavelets built from the unitary irreducible representation of the affine group of the real line with positive dilation. This example is illuminating and quite promising in view of applications in various domains of physics where it is necessary to take into account an impenetrable barrier, as it is the case in quantum cosmology.

More precisely, in quantum cosmology, we examine the possibility of dealing with gravitational singularities on a quantum level through the use of coherent state or wavelet quantization instead of canonical quantization. We consider for instance the Robertson-Walker metric coupled to a perfect fluid, or more intricate anisotropic metrics (e.g. the Bianchi's). The results already obtained in the simplest model of a gravitational collapse serve as a useful starting point for more complex investigations. The main issue of our approach is the appearance of a quantum centrifugal potential allowing for regularization of the singularity, essential self-adjointness of the Hamiltonian, and unambiguous quantum dynamical evolution.

**Nonabelian gauge theories and confinement **[J. Serreau]

The understanding of the long distance aspects of the theory of strong interactions is among the most important open questions of high-energy physics. In particular, the quantitative description of confinement in non abelian gauge theories remains a major issue. This is due to the fact that standard perturbative methods are not applicable for low momenta due to the existence of a Landau pole in the infrared. To date, numerical calculations on the lattice provide the main tool to address this regime. These have, however a (large but) limited range of application. In particular, they are powerful tools to compute static quantities in the vacuum or at finite temperature but cannot be applied at finite chemical potential or finite magnetic field, nor can they address real-time quantities such as scattering rates or transport coefficients.

The Theory group of APC studies various aspects of Yang-Mills theories and QCD related to the infrared regime, to confinement and to the description of the quark-gluon plasma.

In contrast to lattice calculations, continuum approaches typically requires one to fix a gauge since they are primarily formulated in terms of the (gauge variant) correlators of the basic fields of the theory. Fixing the gauge in a non abelian gauge theory is, however, not trivial due to the existence of Gribov ambiguities which are notoriously difficult to deal with by means of analytical methods. Standard perturbative techniques, based on the Faddeev-Popov construction, simply ignore this issue. Exploiting a profound analogy between the Gribov problem and disordered systems we have proposed a new approach to gauge-fixing in Yang-Mills theories which consistently takes into account Gribov copies and can be formulated by analytical means. In the widely used case of the Landau gauge, this leads, among other things, to an effective mass for the gluons. The resulting perturbation theory turns out to have no Landau pole and is thus well defined at all energy scales. Perturbative calculations in this context compare well with existing lattice data for gauge-fixed quantities in the Landau gauge. This includes ghost and gluons correlation functions both in the vacuum and at finite temperature, for which lattice calculations show that the gluon indeed acquires an effective mass in the limit of zero momenta, as well as the existence of a phase transition in SU(N) theories.

An alternative approach to strongly coupled field theories being pursued at APC makes use of the holographic Gauge/Gravtiy duality, which allows to map a strongly coupled field theory to a gravitational theory in higher dimensions. This allows to relate phenomena like confinement and the existence of a mass gap to the geometry of the higher dimensional space time. For more details, see the section "Gauge/gravity duality".

**Non-equilibrium quantum field theory **[E. Kiritsis, J. Serreau]

Understanding the dynamics of nonequilibrium quantum fields is of great relevance in a wide range of physical problems ranging from early-Universe cosmology to high-energy physics or to the study of an ultracold quantum gas or strongly correlated systems in solid state physics. Topical examples include the description of particle production and reheating at the end of inflation, the evolution and thermalization of the quark-gluon plasma in high energy heavy ion collisions, or the nonequilibrium dynamics of Bose-Einstein condensates.

Despite their vastly different energy scales, these systems share many similarities and their study often require the use of similar techniques. The description of nonequilibrium systems poses specific technical difficulties since usual approximation schemes in quantum field theory are generically plagued by spurious secular terms which grow unbounded with time. In particular, the description of far-from-equilibrium quantum fields requires the use of specific techniques.

Far-from-equilibrium dynamics and two-particle-irreducible (2PI) techniques (J. Serreau)

We study various resummation techniques in this context, for instance based on two-particle-irreducible (2PI) methods. Our efforts concern both the formal aspects of such techniques and their applications to various physical problems. Examples of formal developments include nonperturbative approximation schemes in the 2PI formalism (such as 1/N expansions), the 2PI renormalization theory, or the application of 2PI techniques to gauge theories. Applications range from fundamental issues in nonequilibrium quantum field theory, such as the description of quantum decoherence, entropy production and thermalization from first principles, to more specific questions such as the explosive particle production and turbulent dynamics at the end of inflation in early-Universe cosmology.

Non-equilibrium physics from the AdS/CFT correspondence (E. Kiritsis)

The AdS/CFT (holographic) correspondence used gravitational physics to describe strongly coupled semiclassical QFTs. It is extremely well suited to address a host of non-equilibrium questions, like real time physics, transport coefficients, the physics of fast quenches of QFTs, real time (dynamical) critical phenomena, the approach to thermal equilibrium (thermalization) etc. Several such contexts are studied by APC researchers, in particular thermalization in strongly coupled gauge theories, the Langevin diffusion of strongly coupled probes and associated Fokker-Planck dynamics, dynamical quasi-equilibria, and quenches.

**Higher Spin theory **[J. Mourad]

The theory of Higher-Spin Gauge Fields is an enticing and still largely unexplored corner of Field Theory. On the one hand, starting from spin two, the potential coupling constants have negative mass dimensions leading to power counting nonrenormalisable theories. On the other hand, higher spin particles have a crucial role in the softness of string interactions at high energies; the infinite tower of massive higher-spin states provides a regularisation in the ultraviolet. In this perspective, we have studied some open issues concerning free higher-spin fields of mixed symmetry. In particular the fermionic action is determined for the first time and the equations are reduced to the Fronsdal-Labastida form.

The AdS/CFT correspondence can potentially give important hints concerning consistent interacting higher spins fields. In fact, one of the most remarkable holographic correspondences is the conjecture relating an interacting higher-spin theory in AdS to a boundary free scalar theory. This conjecture allows, in principle, to relate the observables of the higher-spin theory to observables in the free CFT coupled to external higher-spin sources. Since the CFT is free one expects to deduce many features of the higher-spin theory and to better understand the Vasiliev system, the candidate of the AdS theory. Despite many checks, the state of affairs is still unsatisfactory because a systematic comparison is still lacking. We proposed to start a systematic study starting from the reasonable assumption that the higher-spin theory can be described as a series in the coupling constant with the first term being the free Fronsdal action. So we undertook the determination of the free on-shell Fronsdal action as a functional of the boundary data. This is the object to be compared with the quadratic part of the CFT effective action which we have also studied in detail.

**Gauge/Gravity Duality and applications **[E. Kiritsis, F. Nitti]

The Gauge/Gravity duality, or Holographic correspondence, is one of the deepest insights that have arisen from string theory in the past 15-20 years, and it has provided a new way of looking at quantum field theories. The duality is a conjecture that states the equivalence between a quantum field theory on one side, and a gravitational theory (or string theory) in a higher-dimensional, curved space-time on the other side. It provides a new link between quantum field theory and geometry, and for this reason it lies at the interface between quantum field theory, string theory and general relativity. At the same time, the holographic duality provides a valuable calculational tool: when the field theory side of the correspondence is strongly coupled and has a large number of degrees of freedom, the gravity side becomes classical and can be described with standard General Relativity.

There is a large amount of ongoing research focused on applying the correspondence to strongly coupled field theories such as QCD, and applications have been suggested in the context of strongly interacting condensed-matter systems such as high-temperature superconductors and strongly correlated quantum Fermi systems. The gauge/gravity duality has also revealed an intriguing relation between the gravitational Einstein equations and the non-linear equations of fluid dynamics. In this context, dissipation in hydrodynamic systems have been related to the physics and geometry of black hole horizons.

Within the APC theory group, the research on the gauge/gravity duality is focused mainly on the following topics:

• Bottom-up Holographic models for QCD

The original version of the correspondence relates string theory on a particular ten-dimensional space-time (namely the product of five-dimensional Anti-de Sitter space and a five-dimensional sphere) to a relative of QCD, i.e. the maximally super-symmetric Yang-Mills theory in four dimensions. To get closer to real-world QCD, one may adopt a phenomenological approach: using the holographic dictionary to engineer simple theories which match the properties found in QCD (confinement, mass gap, and running of the coupling constant). This approach has allowed constructing holographic theories that provide a quantitative match of many QCD observables, and allow computing dynamical features which are hard to obtain with different methods. Another active research subject in this context is the construction of holographic duals of QCD-like theories with a large number of flavors and the understanding of their phase diagram at finite temperature and baryon-number density.

• Holography and strongly interacting condensed matter systems

Certain condensed matter system exhibit phase transitions which are governed by strongly interacting quantum critical points, and exhibit non-relativistic scaling behavior in the infrared regime. Using the gauge/gravity duality it has been proposed to describe this behavior in terms of higher dimensional space-times with unconventional scaling isometries (i.e. in which space and time have different scaling dimensions). The classification and analysis of these space-times, their realisation as solutions of Einstein-Maxwell theories coupled to scalar fields, as well as the understanding of their finite temperature and density phase diagram is one of the research directions which is pursued in the APC theory group.

• Holographic Renormalization Group

The Renormalization Group (RG) describes how quantum field theories behave under a change of the energy scale, and in particular how the coupling constants evolve as a function of energy. In the gauge/gravity duality, the RG has a geometric réalisation, and the flow between quantum theories is realised as geometric flows between curved space-times. Understanding precisely the way this map is explicitly realized.

• Solving non-equilibrium problems in strongly coupled QFTs (as described in an earlier section)

Using strongly coupled QFTs in cosmological applications. This effort goes in two directions. The first is to calculate the induced action for QFT fields and gravity due to strong coupling effects. This uses the techniques and tools mentioned above for the Holographic Renormalization group section. The second is to study the cosmological physics associated with such dynamics, and its implications for observations in cosmology.