Seiberg-Witten geometry of four-dimensional N = 2 SO–USp quiver gauge theories

Zhang, Xinyu

doi:10.1103/PhysRevD.100.125015

Title: Seiberg-Witten geometry of four-dimensional $N = 2$ SO–USp quiver gauge theories

Abstract

We apply the instanton counting method to study a class of four-dimensional N=2 supersymmetric quiver gauge theories with alternating SO and USp gauge groups. We compute the partition function in the Ω-background and express it as functional integrals over density functions. Applying the saddle point method, we derive the limit shape equations which determine the dominant instanton configurations in the flat space limit. The solution to the limit shape equations gives the Seiberg-Witten geometry of the low energy effective theory. As an illustrating example, we work out explicitly the Seiberg-Witten geometry for linear quiver gauge theories. Our result matches the Seiberg-Witten solution obtained previously using the method of brane constructions in string theory.

Authors:

Publication Date:: Tue Dec 17 00:00:00 EST 2019

Research Org.:: Rutgers Univ., Piscataway, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1579599

Alternate Identifier(s):: OSTI ID: 1579556

Grant/Contract Number:: SC0010008

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 12; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric field theories

Citation Formats


                    Zhang, Xinyu. Seiberg-Witten geometry of four-dimensional N = 2 SO–USp quiver gauge theories.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.125015.

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                    Zhang, Xinyu. Seiberg-Witten geometry of four-dimensional N = 2 SO–USp quiver gauge theories.  United States.  https://doi.org/10.1103/PhysRevD.100.125015

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                    Zhang, Xinyu. Tue .  
"Seiberg-Witten geometry of four-dimensional N = 2 SO–USp quiver gauge theories".  United States.  https://doi.org/10.1103/PhysRevD.100.125015.

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@article{osti_1579599,

  title        = {Seiberg-Witten geometry of four-dimensional N = 2 SO–USp quiver gauge theories},

  author       = {Zhang, Xinyu},

  abstractNote = {We apply the instanton counting method to study a class of four-dimensional N=2 supersymmetric quiver gauge theories with alternating SO and USp gauge groups. We compute the partition function in the Ω-background and express it as functional integrals over density functions. Applying the saddle point method, we derive the limit shape equations which determine the dominant instanton configurations in the flat space limit. The solution to the limit shape equations gives the Seiberg-Witten geometry of the low energy effective theory. As an illustrating example, we work out explicitly the Seiberg-Witten geometry for linear quiver gauge theories. Our result matches the Seiberg-Witten solution obtained previously using the method of brane constructions in string theory.},

  doi          = {10.1103/PhysRevD.100.125015},

  journal      = {Physical Review D},

  number       = 12,

  volume       = 100,

  place        = {United States},

  year         = {Tue Dec 17 00:00:00 EST 2019},

  month        = {Tue Dec 17 00:00:00 EST 2019}

}

Copy to clipboard

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Title: Seiberg-Witten geometry of four-dimensional N = 2 SO–USp quiver gauge theories

Abstract

Citation Formats

ABCD of Instantons journal, September 2004

Tinkertoys for the twisted D-series journal, April 2015

Splitting of surface defect partition functions and integrable systems journal, January 2019

Quantum Geometry and Quiver Gauge Theories journal, January 2018

BPS/CFT correspondence IV: sigma models and defects in gauge theory journal, July 2018

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters journal, March 2016

A note on instanton counting for N =2 gauge theories with classical gauge groups journal, May 2004

M-theory and Seiberg-Witten curves: orthogonal and symplectic groups journal, October 1997

Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry journal, January 2010

Instantons on Noncommutative ℝ 4 , and (2,0) Superconformal Six Dimensional Theory journal, November 1998

N = 2 supersymmetric gauge theories, branes and orientifolds journal, December 1997

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD journal, December 1994

Seiberg-Witten Prepotential from Instanton Counting journal, January 2003

BPS/CFT Correspondence III: Gauge Origami Partition Function and qq-Characters journal, December 2017

Surface operators and separation of variables journal, January 2016

Instantons on S4 and CP2, rank stabilization, and Bott periodicity journal, March 2000

Supersymmetric Vacua and Bethe Ansatz journal, July 2009

Localization with a surface operator, irregular conformal blocks and open topological string journal, January 2012

Instanton counting with a surface operator and the chain-saw quiver journal, June 2011

Intersecting surface defects and two-dimensional CFT journal, August 2017

Deformed Seiberg-Witten curves for ADE quivers journal, January 2013

Darboux coordinates, Yang-Yang functional, and gauge theory journal, July 2011

Towards a 4d/2d correspondence for Sicilian quivers journal, October 2011

An SU(2) anomaly journal, November 1982

{\mathcal N}=2 S-duality via outer-automorphism twists journal, April 2011

Intersecting surface defects and instanton partition functions journal, July 2017

Orientifolds, branes, and duality of 4D gauge theories journal, November 1997

The omega deformation, branes, integrability and Liouville theory journal, September 2010

BPS/CFT correspondence II: Instantons at crossroads, moduli and compactness theorem journal, January 2017

From SO/Sp instantons to W-algebra blocks journal, March 2011

Classification of 4d $ \mathcal{N} $ =2 gauge theories journal, December 2013

Cubic curves from instanton counting journal, March 2006

Six-dimensional D N theory and four-dimensional SO-USp quivers journal, July 2009

Tinkertoys for the D N series journal, February 2013

Affine SL(2) Conformal Blocks from 4d Gauge Theories journal, September 2010

Instantons on Quivers and Orientifolds journal, October 2004

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory journal, September 1994

Saddle point equations in Seiberg-Witten theory journal, October 2004

Construction of instantons journal, March 1978

Title: Seiberg-Witten geometry of four-dimensional $N = 2$ SO–USp quiver gauge theories

ABCD of Instantons
journal, September 2004

Tinkertoys for the twisted D-series
journal, April 2015

Splitting of surface defect partition functions and integrable systems
journal, January 2019

Quantum Geometry and Quiver Gauge Theories
journal, January 2018

BPS/CFT correspondence IV: sigma models and defects in gauge theory
journal, July 2018

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
journal, March 2016

A note on instanton counting for N =2 gauge theories with classical gauge groups
journal, May 2004

M-theory and Seiberg-Witten curves: orthogonal and symplectic groups
journal, October 1997

Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry
journal, January 2010

Instantons on Noncommutative ℝ 4 , and (2,0) Superconformal Six Dimensional Theory
journal, November 1998

N = 2 supersymmetric gauge theories, branes and orientifolds
journal, December 1997

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

BPS/CFT Correspondence III: Gauge Origami Partition Function and qq-Characters
journal, December 2017

Surface operators and separation of variables
journal, January 2016

Instantons on S4 and CP2, rank stabilization, and Bott periodicity
journal, March 2000

Supersymmetric Vacua and Bethe Ansatz
journal, July 2009

Localization with a surface operator, irregular conformal blocks and open topological string
journal, January 2012

Instanton counting with a surface operator and the chain-saw quiver
journal, June 2011

Intersecting surface defects and two-dimensional CFT
journal, August 2017

Deformed Seiberg-Witten curves for ADE quivers
journal, January 2013

Darboux coordinates, Yang-Yang functional, and gauge theory
journal, July 2011

Towards a 4d/2d correspondence for Sicilian quivers
journal, October 2011

An SU(2) anomaly
journal, November 1982

{\mathcal N}=2 S-duality via outer-automorphism twists
journal, April 2011

Intersecting surface defects and instanton partition functions
journal, July 2017

Orientifolds, branes, and duality of 4D gauge theories
journal, November 1997

The omega deformation, branes, integrability and Liouville theory
journal, September 2010

BPS/CFT correspondence II: Instantons at crossroads, moduli and compactness theorem
journal, January 2017

From SO/Sp instantons to W-algebra blocks
journal, March 2011

Classification of 4d $ \mathcal{N} $ =2 gauge theories
journal, December 2013

Cubic curves from instanton counting
journal, March 2006

Six-dimensional D _N theory and four-dimensional SO-USp quivers
journal, July 2009

Tinkertoys for the D N series
journal, February 2013

Affine SL(2) Conformal Blocks from 4d Gauge Theories
journal, September 2010

Instantons on Quivers and Orientifolds
journal, October 2004

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994

Saddle point equations in Seiberg-Witten theory
journal, October 2004

Construction of instantons
journal, March 1978