#### 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.

Done