T-dualities in gauged linear sigma models

TL;DR

This paper explores non-Abelian T-dualities in two-dimensional gauged linear sigma models with various supersymmetries, analyzing dual geometries, effective potentials, and non-perturbative effects, revealing potential new symmetries in physical theories.

Contribution

It provides a detailed analysis of non-Abelian T-dualities in GLSMs with different supersymmetries, including explicit computations and symmetry-based insights into dual geometries and non-perturbative effects.

Findings

Dual geometries match effective potentials at the conifold point.

Non-perturbative corrections are consistent across dual models.

Potential new symmetries between physical theories are identified.

Abstract

We describe non-Abelian T-dualities for $\mathcal{N} = 2$ two dimensional gauged linear sigma model (GLSM). We start with the case of left and right $(2, 2)$ supersymmetry (SUSY), $U(1)$ gauge group, and global non-Abelian symmetries. Our analysis applies to the specialization of the GLSM with the global group $SU(2)\times SU(2)$, whose original model is the resolved conifold. We analyze the dual model and compute the periods on the dual geometry, matching the effective potential for the $U(1)$ gauge field, and discuss the coincident singularity at the conifold point. We further present the non-Abelian T-dualization of models with $(0,2)$ SUSY, analyzing the case of global symmetry $SU(2)$. In this case the full non-Abelian duality can be solved. The dual geometries with and without non-perturbative corrections to the superpotential coincide. The structure of the dual non-perturbative corrections employed are determined based on symmetry arguments. The non-Abelian T-dualities reviewed here lead to potential new symmetries between physical theories.