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arXiv · 1609.07443

Localization on $AdS_2\times S^1$

Justin R. David·Edi Gava·Rajesh Kumar Gupta·Kumar Narain
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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 $S^3$.

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Justin R. David, Edi Gava, Rajesh Kumar Gupta, Kumar Narain. 2016-09-23. Localization on $AdS_2\times S^1$. https://doi.org/10.1007/jhep03(2017)050

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