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Modified supersymmetric indices in AdS$_3$/CFT$_2$
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abstract
We consider the $\mathcal{N}=(2,2)$ AdS$_3$/CFT$_2$ dualities proposed by Eberhardt, where the bulk geometry is AdS$_3\times(S^3\times T^4)/\mathbb{Z}_k$, and the CFT is a deformation of the symmetric orbifold of the supersymmetric sigma model $T^4/\mathbb{Z}_k$ (with $k=2,\ 3,\ 4,\ 6$). The elliptic genera of the two sides vanish due to fermionic zero modes, so for microstate counting applications one must consider modified supersymmetric indices. In an analysis similar to that of Maldacena, Moore, and Strominger for the standard $\mathcal{N}=(4,4)$ case of $T^4$, we study the appropriate helicity-trace index of the boundary CFTs. We encounter a strange phenomenon where a saddle-point analysis of our indices reproduces only a fraction (respectively $\frac{1}{2},\ \frac{2}{3},\ \frac{3}{4},\ \frac{5}{6}$) of the Bekenstein-Hawking entropy of the associated macroscopic black branes.
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Cited by 1 Pith paper
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Topologically charged BPS microstates in AdS$_3$/CFT$_2$
Modified helicity-trace indices for charged sectors of AdS3/CFT2 produce the Cardy/Bekenstein-Hawking entropy, reproducing Larsen-Martinec in the T^4 case and resolving the earlier HS2 mismatch in half-integer winding...
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