Topologically charged BPS microstates in AdS3/CFT2

A bstract In the standard $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (4, 4) AdS 3 /CFT 2 with sym N ( T 4 ), as well as the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (2, 2) Datta-Eberhardt-Gaberdiel variant with sym N ( T 4 / 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (4, 4) case we reproduce the microstate matching of Larsen and Martinec. In the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (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.