On Super Non-Abelian T-Duality of Symmetric and Semi-Symmetric Coset Sigma Models

TL;DR

This paper reviews super non-Abelian T-Duality in symmetric and semi-symmetric coset sigma models, identifies obstructions in the dualization process, and provides explicit solutions for two specific models.

Contribution

It analyzes the algebraic approach to super non-Abelian T-Duality, identifies conditions for successful dualization, and explicitly solves for dual actions in two models.

Findings

Identifies three cases where T-duality can be successfully applied.

Provides explicit dual actions for symmetric and semi-symmetric coset models.

Highlights an obstruction in integrating out gauge fields in certain models.

Abstract

We review the algebraic approach to super non-Abelian T-Duality considered in [1], focusing on symmetric and semi-symmetric coset spaces on $G/H$. We discuss a potential impediment, appearing in these models when integrating out the gauge field in favour of the dual variables. This process cannot be performed in general and we isolate the obstruction, highlighting three cases in which a solution can be found. After writing the T-dual action we provide solution for two specific models. The first based on the symmetric space $S^{3} \simeq SO(4)/SO(3)$, well-known in the literature, the second on the semi-symmetric coset $OSp(1|2)/SO(1,1)$, a Green-Schwarz-like string sigma model satisfying the supergravity torsion constraints.