Self-duality of the D1-D5 near-horizon

We explore fermionic T-duality and self-duality in the geometry AdS(3) x S-3 x T-4 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 AdS(3) T-dualities, four fermionic T-dualities and either two additional T-dualities along T-4 or two T-dualities along S-3. 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.