Self-duality of the D1-D5 near-horizon

We explore fermionic T-duality and self-duality in the geometry AdS ₃×S ³×T ⁴ in type IIB supergravity. We explicitly construct the Killing spinors and the fermionic Tduality 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 Tduality not commuting. Finally, we argue that fermionic T-duality may be extended to CY ₂ = K3, a setting where we cannot explicitly construct the Killing spinors.