Fermionic T-Duality of $AdS_n \times S^n (\times S^n) \times T^m$ using IIA Supergravity

TL;DR

This paper demonstrates the self-duality of certain AdS x S x T string backgrounds under combined bosonic and fermionic T-dualities using supergravity methods, revealing the behavior of RR fields and the necessity of T-duality along specific directions.

Contribution

It explicitly applies fermionic Buscher rules to analyze the self-duality of complex AdS x S x T backgrounds at the supergravity level, including RR field transformations.

Findings

AdS2 x S2 x T6 background is self-dual under T-duality.

AdS d x S d x S d x T^{10-3d} backgrounds are also self-dual.

T-duality along certain torus directions is essential for self-duality.

Abstract

We show that the string backgrounds AdS2 x S2 x T6 and AdSd x Sd x Sd x T{10 - 3d} (d = 2, 3) are self-dual under a series of bosonic and fermionic T-dualities. We do this using the fermionic Buscher rules derived by Berkovits and Maldacena, thus working at the level of the supergravity fields. This allows us to explicitly track the behaviour of the RR fields, from which we see that we need T-duality along some torus directions. For the AdS x S x S cases, which contain cosets of D(2,1;alpha), it is necessary to perform bosonic T-duality along some complexified Killing spinors in one of the spheres.