Centre de Physique Théorique


Vendredi 8 juin 2018

14h00 – 15h00, Amphi 5 du CPT

Chern-Weil theorem and boundary terms in gravity actions

Nelson MERINO (APC, Paris)

There are two mathematical approaches that are commonly used in the construction of gravity theories : tensorial and Cartan language. It is usually said that they are completely equivalent and that the translation between them should be evident. However, as we show in this work, there are cases where a result in one side is not clearly understood in the other, because the translation is not obvious. This is the case of the Katz procedure, which being constructed in the tensorial language, allows to have a well-defined variational principle and to define finite conserved charges in general relativity. Up to now, it was not known how this method reads in Cartan language, neither how it could be generalized to more general theories (e.g., Einstein-Gauss-Bonnet and Lovelock gravity). In this work we use the Chern-Weil theorem and a topological-algebraic structure called transgression form to provide the translation of the Katz boundary term into the Cartan language. As a consequence, this gives us a guideline to make the generalization of the Katz procedure for a generic Lovelock gravity.