On Integrable Backgrounds Self-dual under Fermionic T-duality

TL;DR

The paper investigates when fermionic T-duality augments integrable Green-Schwarz sigma-models on RR AdS backgrounds with self-duality under a combined bosonic/fermionic T-duality. It shows PSU cosets such as $AdS_2\times S^2$ and $AdS_3\times S^3$ are self-dual through explicit Buscher-like procedures and $\ ext{Z}_4$ automorphisms, while ortho-symplectic cosets (non-critical $AdS_2$, $AdS_4$, and $AdS_4\times\mathbb{C}P^3$) fail due to a singular fermionic sector arising from the Cartan-Killing bilinear form and R-symmetry structure. A general algebraic framework is proposed: the invertibility of a fermionic coupling matrix $M$ (emerging in the gauge-field elimination) determines the existence of a fermionic T-dual, with PSU models typically yielding invertible $M$ and OSpp models yielding singular $M$, thus explaining the observed non-self-duality. These results highlight that dual superconformal symmetry is not automatic in AdS/CFT contexts, even when the underlying theory is integrable.

Abstract

We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma-models on AdS backgrounds with Ramond-Ramond fluxes in various dimensions. We show that sigma-models based on supercosets of PSU supergroups, such as AdS_2 \times S^2 and AdS_3 \times S^3 are self-dual under fermionic T-duality, while supercosets of OSp supergroups such as non-critical AdS_2 and AdS_4 models, and the critical AdS_4 \times CP^3 background are not. We present a general algebraic argument to when a supercoset is expected to have a fermionic T-duality symmetry, and when it will fail to have one.