Séminaire de Physique ThéoriqueThe Casimir energy of supersymmetric field theories via localization and holography
Davide Cassani (LPTHE, Paris 6)
Thursday 28 April 2016 14:00 - Tours - Salle 1180 (Bât E2)
A main challenge in the study of quantum field theories is to develop new, non-perturbative methods giving access to the strongly coupled regime. Recently, progress in this direction has been fostered by the technique of localization, which allows to evaluate exactly, i.e. at any value of the coupling, the path integral of supersymmetric quantum field theories in curved space. After an introduction to the topic, I will focus on four-dimensional manifolds with S^1 x S^3 topology and present the localization computation of the partition function for a general supersymmetric quantum field theory. From the result I will extract the Casimir energy of the theory on the three-sphere. While generically the Casimir energy depends on the renormalization scheme, I will show that in the presence of supersymmetry it becomes an intrinsic observable. I will conclude emphasizing the relevance of these results for the AdS/CFT correspondence and pointing out an open problem in supersymmetric holography.