Séminaire de Physique ThéoriqueTwo-dimensional supersymmetric gauge theories and non-Kähler geometry
Dan Israël (LPTHE, Paris 6)
Thursday 04 February 2016 14:00 - Tours - Salle 1180 (Bât E2)
Non-linear sigma-models on Kähler manifolds can be obtained through the low-energy dynamics of two-dimensional supersymmetric gauge theories, following the seminal work of Witten; this has led in particular to important insights about mirror symmetry. In this seminar, I will describe recent advances in understanding sigma-models on non-Kähler geometries, which are relevant for string compactifications with flux, by extending this framework to classically non-gauge invariant theories. As an illustration I will show how to compute a supersymmetric index, counting space-time BPS states in an important class of models, using supersymmetric localization. On the physical side it provides a valuable tool to broaden our knowledge of strong/weak coupling dualities in string theory, and on the mathematical side interesting connections between algebraic geometry and number theory can be made.