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Title: Non Abelian T-duality in Gauged Linear Sigma Models

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 inmore » 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. Finally, we analyze the dual models via the geometry of their susy vacua.« less
Authors:
ORCiD logo [1] ;  [2] ; ORCiD logo [3] ;  [4]
  1. Univ. de Guanajuato, Guanajuato (Mexico). Dept. de Fisica, Division de Ciencias e Ingenierias; Univ. of the Witwatersrand, Johannesburg (South Africa). Mandelstam Inst. for Theoretical Physics, School of Physics, and National Inst. for Theoretical Physics
  2. Univ. de Guanajuato, Guanajuato (Mexico). Dept. de Fisica, Division de Ciencias e Ingenierias; Univ. Autonoma de Chiapas, Chiapas (Mexico). Investigador Catedra CONACyT, Facultad de Ciencias en Fisica y Matematicas
  3. Univ. of Michigan, Ann Arbor, MI (United States). Leinweber Center for Theoretical Physics, Randall Lab. of Physics; Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
  4. Univ. de Guanajuato, Guanajuato (Mexico). Dept. de Fisica, Division de Ciencias e Ingenierias; Univ. de Guanajuato, Guanajuato (Mexico). Dept. de Ciencias Naturales y Exactas
Publication Date:
Grant/Contract Number:
SC0017808; 271904
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Duality in Gauge Field Theories; Sigma Models; String Duality; Supersymmetric Gauge Theory
OSTI Identifier:
1457332
Alternate Identifier(s):
OSTI ID: 1457686

Bizet, Nana Cabo, Martinez-Merino, Aldo, Zayas, Leopoldo A. Pando, and Santos-Silva, Roberto. Non Abelian T-duality in Gauged Linear Sigma Models. United States: N. p., Web. doi:10.1007/JHEP04(2018)054.
Bizet, Nana Cabo, Martinez-Merino, Aldo, Zayas, Leopoldo A. Pando, & Santos-Silva, Roberto. Non Abelian T-duality in Gauged Linear Sigma Models. United States. doi:10.1007/JHEP04(2018)054.
Bizet, Nana Cabo, Martinez-Merino, Aldo, Zayas, Leopoldo A. Pando, and Santos-Silva, Roberto. 2018. "Non Abelian T-duality in Gauged Linear Sigma Models". United States. doi:10.1007/JHEP04(2018)054. https://www.osti.gov/servlets/purl/1457332.
@article{osti_1457332,
title = {Non Abelian T-duality in Gauged Linear Sigma Models},
author = {Bizet, Nana Cabo and Martinez-Merino, Aldo and Zayas, Leopoldo A. Pando and Santos-Silva, Roberto},
abstractNote = {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. Finally, we analyze the dual models via the geometry of their susy vacua.},
doi = {10.1007/JHEP04(2018)054},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}