On Integrable Backgrounds Self-dual under Fermionic T-duality

TL;DR

This paper investigates the fermionic T-duality symmetry in integrable Green-Schwarz sigma-models on various AdS backgrounds, identifying which models are self-dual and providing algebraic criteria for this property.

Contribution

It demonstrates which supercoset sigma-models are self-dual under fermionic T-duality and offers a general algebraic framework to predict this symmetry.

Findings

Supercosets of PSU supergroups are self-dual under fermionic T-duality.

Supercosets of OSp supergroups generally are not self-dual.

An algebraic criterion predicts when a supercoset has fermionic T-duality symmetry.

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.