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arXiv · 2301.08084

Localization on $AdS_3 \times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity

Axel Ciceri·Imtak Jeon·Sameer Murthy
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Abstract

We begin to develop the formalism of localization for the functional integral of supergravity on $AdS_3 \times S^2$. We show how the condition of supersymmetry in the Euclidean $\mathbb{H}^3/\mathbb{Z} \times S^2$ geometry naturally leads to a twist of the S$^2$ around the time direction of $AdS_3$. The twist gives us a five-dimensional Euclidean supergravity background dual to the elliptic genus of $(0,4)$ SCFT$_2$ at the semiclassical level. On this background we set up the off-shell BPS equations for one of the Killing spinors, such that the functional integral of five-dimensional Euclidean supergravity on $\mathbb{H}^3/\mathbb{Z} \times S^2$ localizes to its space of solutions. We obtain a class of solutions to these equations by lifting known off-shell BPS solutions of 4-dimensional supergravity on $AdS_2 \times S^2$. In order to do this consistently, we construct and use a Euclidean version of the off-shell 4d/5d lift of arxiv:1112.5371, which could be of independent interest.

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Axel Ciceri, Imtak Jeon, Sameer Murthy. 2023-01-19. Localization on $AdS_3 \times S^2$ I: the 4d/5d connection in off-shell Euclidean supergravity. https://doi.org/10.1007/jhep07(2023)218

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