Perturbative dynamics of massive gluons

Lattice simulations of Yang-Mills theories and QCD in the Landau gauge have

demonstrated that the gluon propagator saturates at vanishing momentum. This can

be modeled by a massive deformation of the corresponding Faddeev-Popov

Lagrangian known as the Curci-Ferrari model. The latter does not modify the known

ultraviolet regime of the theory and provides a successful perturbative description of

essential aspects of the non-Abelian dynamics in the infrared regime, where, in

Galileon p-form theories

I will discuss the generalization to p-forms of the Galileon idea: to
construct the most general theory of an (abelian gauge invariant) p-form
with (strictly) second order field equations. Such theory have recently be
fully classified for space-time dimension strictly smaller than 12. The
covariantization of these theories will also be discussed.

Chern-Weil theorem, Lovelock Lagrangians in critical dimensions and boundary terms in gravity actions

We show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid, manifold whose geometry we construct explicitely. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form.


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