Abstract
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\_2S^1\$ and determine the localizing Lagrangian for \$N=2\$
supersymmetric Chern-Simons theory on \$AdS\_2S^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\_2S^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\$.
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