Hall 123

Supersymmetric Localization on AdS_2 x S^1

Rajesh Gupta

King's College London

Supersymmetric localization is a powerful technique to evaluate observables in supersymmetric quantum field theories exactly. The method
has been used extensively in supersymmetric quantum field theory defined on curved but compact spaces. In this talk I will discuss the application of the method on a non compact space. Quantum field theories on spaces of the form AdS_n x S^m are relevant in evaluating black hole entropy as well as entanglement entropy across spherical entangling surfaces in conformal field theories on flat space. We study supersymmetric localization on AdS_2 x S^1 in N = 2 supersymmetric Chern-Simons theory. We evaluate the partition function of N = 2 supersymmetric Chern-Simons theory where the radius of S^1 is q times that of AdS_2. With boundary conditions on AdS_2 x S^1 which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in AdS_2, the result for the partition function precisely agrees with that of the theory on the q-fold covering of S^3.