Localization on AdS2 x S1

Conformal symmetry relates the metric on AdS(2) x S-1 to that of S-3. This implies that under a suitable choice of boundary conditions for fields on AdS(2) the partition function of conformal field theories on these spaces must agree which makes AdS(2) x S-1 a good testing ground to study localization on non-compact spaces. We study supersymmetry on AdS(2) x S-1 and determine the localizing Lagrangian for N - 2 supersymmetric ChernSimons theory on AdS(2)xS(1). We evaluate the partition function of N - 2 supersymmetric Chern- Simons theory on AdS(2) x S-1 using localization, where the radius of S1 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.