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

We review the algebraic approach to super non-Abelian T-Duality considered in [1], focusing on symmetric and semi-symmetric coset spaces on $G\mathrm{/}H$. 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 $S^3\simeq SO(4)\mathrm{/}SO(3)$, well-known in the literature, the second on the semi-symmetric coset $OSp(1\mathrm{\mid }2)\mathrm{/}SO(1,1)$, a Green-Schwarz-like string sigma model satisfying the supergravity torsion constraints.