%0 Generic %1 David2016Localization %A David, Justin R. %A Gava, Edi %A Gupta, Rajesh K. %A Narain, Kumar %D 2016 %K ads2, jc, localization %T Localization on \$AdS\_2S^1\$ %U http://arxiv.org/abs/1609.07443 %X 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\$.

@misc{David2016Localization, abstract = {Conformal symmetry relates the metric on \$AdS\_2 \times 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 \times S^{1}\$ a good testing ground to study localization on non-compact spaces. We study supersymmetry on \$AdS\_2\times S^1\$ and determine the localizing Lagrangian for \${\cal N}=2\$ supersymmetric Chern-Simons theory on \$AdS\_2\times S^1\$. We evaluate the partition function of \${\cal N}=2\$ supersymmetric Chern-Simons theory on \$AdS\_2 \times S^1\$ using localization, where the radius of \$S^1\$ is \$q\$ times that of \$AdS\_2\$. With boundary conditions on \$AdS\_2\times 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\$.}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {David, Justin R. and Gava, Edi and Gupta, Rajesh K. and Narain, Kumar}, biburl = {https://www.bibsonomy.org/bibtex/246f9e987782d6d640406dcc5fbacc262/acastro}, citeulike-article-id = {14146512}, citeulike-linkout-0 = {http://arxiv.org/abs/1609.07443}, citeulike-linkout-1 = {http://arxiv.org/pdf/1609.07443}, day = 23, eprint = {1609.07443}, interhash = {16648047554eea8b7c188078e1f67198}, intrahash = {46f9e987782d6d640406dcc5fbacc262}, keywords = {ads2, jc, localization}, month = sep, posted-at = {2016-09-26 13:54:35}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Localization on \$AdS\_2\times S^1\$}}, url = {http://arxiv.org/abs/1609.07443}, year = 2016 }