Eur. Phys. J. C (2025) 85: 10
https://doi.org/10.1140/epjc/s10052-024-13677-7

Regular Article - Theoretical Physics

Non Abelian dual of the resolved conifold gauged linear sigma model

¹ División de Ciencias e Ingenierías, Departamento de Física, Universidad de Guanajuato, Loma del Bosque 103, C.P. 37150, León, Guanajuato, Mexico
² Departamento Ciencias Naturales y Exactas, CUValles, Universidad de Guadalajara, Carretera Guadalajara-Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco, Mexico

^a nana@fisica.ugto.mx

Received: 1 September 2024
Accepted: 2 December 2024
Published online: 8 January 2025

Abstract

We consider T-dualities arising from global symmetries in two dimensional Gauged Linear Sigma Models (GLSMs). The model has $\mathcal{N}=(2,2)$ supersymmetry, U(1) gauge group, and leads to the susy vacuum of the resolved conifold. It possesses the non-Abelian global symmetry $SU(2)\times SU(2)$. A non-Abelian T-duality can be constructed, which can be described by gauging the global non-Abelian symmetry. This leads to a dual action, in terms of the dual model’s Kähler and superpotential terms, which include a dependence on twisted chiral superfields. The effective superpotentials for the U(1) vector superfield in the original and dual models are matched, determining the instanton corrections of the dual action. This is an important observable in the UV regime, which establishes the duality. We obtain the supersymmetry vacuum solution of the dual model in three cases: first, in an Abelian direction inside $SU(2)\times SU(2)$; second, for an Abelian direction considering instanton corrections; and finally, for a semi-chiral non-Abelian vector superfield. The dual geometry for the cases without instanton corrections (SUSY vacuum space) is given by $T^5\times \mathbb{R}$. For the duality with instanton corrections, one obtains the vacuum space $T^3\times {\mathbb{R}}^2$, and with IR modifications to the twisted superpotential, one obtains a 3-fold given as a cubic polynomial on ${({\mathbb{C}}^{\times })}^3\times \mathbb{C}$. We discuss the $U{(1)}_A$ axial R-symmetry in the dual model and its possible role.