Localization on AdS2 × S1

A bstract Conformal symmetry relates the metric on AdS 2 × 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 × S 1 a good testing ground to study localization on non-compact spaces. We study supersymmetry on AdS 2 × S 1 and determine the localizing Lagrangian for N = 2 supersymmetric Chern-Simons theory on AdS 2 × S 1 . We evaluate the partition function of N = 2 supersymmetric Chern-Simons theory on AdS 2 × S 1 using localization, where the radius of S 1 is q times that of AdS 2 . With boundary conditions on AdS 2 × 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 .