# T-Duality in $(2,1)$ Superspace

## TL;DR

This paper derives T-duality rules for (2,1) supersymmetric sigma-models, clarifying their geometric structure and showing that obstructions to T-duality are less restrictive than previously thought.

## Contribution

It provides the first explicit T-duality transformation rules in (2,1) superspace and develops a geometric gauging approach for these models.

## Key findings

- Derived T-duality transformation rules in (2,1) superspace
- Clarified the geometric structure of (2,1) sigma models
- Found that obstructions to (2,1) T-duality are weaker than in other models

## Abstract

We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality transformations (including an important refinement) together with diffeomorphisms. We use the gauging of sigma-models in (2,1) superspace, which we review and develop, finding a manifestly real and geometric expression for the gauged action. We discuss the obstructions to gauging (2,1) sigma-models, and find that the obstructions to (2,1) T-duality are considerably weaker.