Topologically charged BPS microstates in AdS$_3$/CFT$_2$

Arash Arabi Ardehali; Hare Krishna

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arXiv · 2411.13824

Topologically charged BPS microstates in AdS$_3$/CFT$_2$

Arash Arabi Ardehali·Hare Krishna

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Abstract

In the standard $\mathcal{N}=(4,4)$ AdS$_3$/CFT$_2$ with $\mathrm{sym}^N(T^4)$, as well as the $\mathcal{N}=(2,2)$ Datta-Eberhardt-Gaberdiel variant with $\mathrm{sym}^N(T^4/\mathbb{Z}_2)$, supersymmetric index techniques have not been applied so far to the CFT states with target-space momentum or winding. We clarify that the difficulty lies in a central extension of the SUSY algebra in the momentum and winding sectors, analogous to the central extension on the Coulomb branch of 4d $\mathcal{N}=2$ gauge theories. We define modified helicity-trace indices tailored to the momentum and winding sectors, and use them for microstate counting of the corresponding bulk black holes. In the $\mathcal{N}=(4,4)$ case we reproduce the microstate matching of Larsen and Martinec. In the $\mathcal{N}=(2,2)$ case we resolve a previous mismatch with the Bekenstein-Hawking formula encountered in the topologically trivial sector by going to certain winding sectors.

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BibTeX RIS

Arash Arabi Ardehali, Hare Krishna. 2024-11-21. Topologically charged BPS microstates in AdS$_3$/CFT$_2$. https://arxiv.org/abs/2411.13824

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