Non Abelian T-duality in Gauged Linear Sigma Models

TL;DR

This paper extends Abelian T-duality in Gauged Linear Sigma Models to non-Abelian cases, providing a new framework for understanding dualities involving non-Abelian symmetries and exploring their geometric and non-perturbative aspects.

Contribution

It introduces a novel formulation of non-Abelian T-duality in GLSMs, generalizing previous Abelian dualities and analyzing their effects on supersymmetric vacua and instanton corrections.

Findings

Reproduces Abelian dual models as a special case.

Derives equations of motion for non-Abelian dualities involving semi-chiral and twisted chiral superfields.

Shows the dual model's effective potential matches the original's in certain configurations.

Abstract

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global $U(1)$ symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as $SU(2)$ they depend on twisted chiral superfields. We solve the equations of motion for an $SU(2)$ gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the $U(1)$ field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.