T-duality without isometry via extended gauge symmetries of 2D sigma models

TL;DR

This paper explores a novel approach to T-duality in string theory that does not require background isometries, using extended gauge symmetries in 2D sigma models to achieve dual models even along non-isometric directions.

Contribution

It introduces a method to perform T-duality without isometries by employing extended gauge symmetries, expanding the scope of dualities in string theory.

Findings

Successfully applied to step 2 nilmanifolds

Derived dual models via extended gauge invariance

Demonstrated feasibility beyond traditional isometric backgrounds

Abstract

Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.