Non Abelian T-duality in Gauged Linear Sigma Models

  • Nana Cabo Bizet
  • Aldo Martínez-Merino
  • Leopoldo A. Pando Zayas
  • Roberto Santos-Silva
Open Access
Regular Article - Theoretical Physics
  • 11 Downloads

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.

Keywords

Duality in Gauge Field Theories Sigma Models String Duality Supersymmetric Gauge Theory 

Notes

Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Departamento de Física, División de Ciencias e IngenieríasUniversidad de GuanajuatoLeónMéxico
  2. 2.Mandelstam Institute for Theoretical Physics, School of Physics, and National Institute for Theoretical PhysicsUniversity of the WitwatersrandJohannesburgSouth Africa
  3. 3.Investigador Cátedra CONACyT, Facultad de Ciencias en Física y MatemáticasUniversidad Autónoma de ChiapasTuxtla GutiérrezMéxico
  4. 4.Leinweber Center for Theoretical Physics, Randall Laboratory of PhysicsThe University of MichiganAnn ArborU.S.A.
  5. 5.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly
  6. 6.Departamento de Ciencias Naturales y ExactasCUValles, Universidad de GuadalajaraAmecaMéxico

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