Self-duality of the D1-D5 near-horizon

TL;DR

This paper investigates fermionic T-duality and self-duality in the AdS3 x S3 x T4 background of type IIB supergravity, demonstrating explicit constructions and conditions for self-duality, and discussing implications for related geometries.

Contribution

It explicitly constructs Killing spinors and identifies the combination of T-dualities that leave the geometry self-dual, also analyzing obstacles like the B-field and extending considerations to K3.

Findings

Geometry is self-dual under specific T-duality combinations.

Presence of B-field obstructs self-duality due to non-commuting S-duality and fermionic T-duality.

Fermionic T-duality potentially extends to K3 surfaces, despite lack of explicit Killing spinors.

Abstract

We explore fermionic T-duality and self-duality in the geometry AdS3 x S3 x T4 in type IIB supergravity. We explicitly construct the Killing spinors and the fermionic T-duality isometries and show that the geometry is self-dual under a combination of two bosonic AdS3 T-dualities, four fermionic T-dualities and either two additional T-dualities along T4 or two T-dualities along S3. In addition, we show that the presence of a B-field acts as an obstacle to self-duality, a property attributable to S- duality and fermionic T-duality not commuting. Finally, we argue that fermionic T-duality may be extended to CY2 = K3, a setting where we cannot explicitly construct the Killing spinors.