’t Hooft defects and wall crossing in SQM

Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W.

doi:10.1007/jhep10(2019)173

Title: ’t Hooft defects and wall crossing in SQM

Abstract

In this paper we study the contribution of monopole bubbling to the expectation value of supersymmetric ’t Hooft defects in Lagrangian theories of class S on R³ × S¹. This can be understood as the Witten index of an SQM living on the world volume of the ’t Hooft defect that couples to the bulk 4D theory. The computation of this Witten index has many subtleties originating from a continuous spectrum of scattering states along the non-compact vacuum branches. We find that even after properly dealing with the spectral asymmetry, the standard localization result for the ’t Hooft defect does not agree with the result obtained from the AGT correspondence. In this paper we will explicitly show that one must correct the localization result by adding an extra term to the standard Jeffrey-Kirwan residue formula. This extra term accounts for the contribution of ground states localized along the non-compact branches. This extra term restores both the expected symmetry properties of the line defect expectation value and reproduces the results derived using the AGT correspondence.

Authors:

^[1]; Dey, Anindya ^[1]; Moore, Gregory W. ^[1]

Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy. NHETC

Publication Date:: Tue Oct 15 00:00:00 EDT 2019

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

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

OSTI Identifier:: 1802017

Grant/Contract Number:: SC0010008

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats


                    Brennan, T. Daniel, Dey, Anindya, and Moore, Gregory W. ’t Hooft defects and wall crossing in SQM.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep10(2019)173.

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                    Brennan, T. Daniel, Dey, Anindya, & Moore, Gregory W. ’t Hooft defects and wall crossing in SQM.  United States.  https://doi.org/10.1007/jhep10(2019)173

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                    Brennan, T. Daniel, Dey, Anindya, and Moore, Gregory W. Tue .  
"’t Hooft defects and wall crossing in SQM".  United States.  https://doi.org/10.1007/jhep10(2019)173.  https://www.osti.gov/servlets/purl/1802017.

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@article{osti_1802017,

  title        = {’t Hooft defects and wall crossing in SQM},

  author       = {Brennan, T. Daniel and Dey, Anindya and Moore, Gregory W.},

  abstractNote = {In this paper we study the contribution of monopole bubbling to the expectation value of supersymmetric ’t Hooft defects in Lagrangian theories of class S on R3 × S1. This can be understood as the Witten index of an SQM living on the world volume of the ’t Hooft defect that couples to the bulk 4D theory. The computation of this Witten index has many subtleties originating from a continuous spectrum of scattering states along the non-compact vacuum branches. We find that even after properly dealing with the spectral asymmetry, the standard localization result for the ’t Hooft defect does not agree with the result obtained from the AGT correspondence. In this paper we will explicitly show that one must correct the localization result by adding an extra term to the standard Jeffrey-Kirwan residue formula. This extra term accounts for the contribution of ground states localized along the non-compact branches. This extra term restores both the expected symmetry properties of the line defect expectation value and reproduces the results derived using the AGT correspondence.},

  doi          = {10.1007/jhep10(2019)173},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 10,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Oct 15 00:00:00 EDT 2019},

  month        = {Tue Oct 15 00:00:00 EDT 2019}

}

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Title: ’t Hooft defects and wall crossing in SQM

Abstract

Citation Formats

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Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions text, January 1997

N = 2 dualities journal, August 2012

ABCD of Instantons journal, September 2004

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories journal, November 2014

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Seiberg-Witten Prepotential from Instanton Counting journal, January 2003

Witten Index and Threshold Bound States of D-Branes text, January 1997

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory journal, July 2010

D-branes, Monopoles and Nahm Equations text, January 1996

Deconstructing (2,0) and Little String Theories journal, January 2003

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Anomalies and odd dimensions journal, September 1985

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D-branes, monopoles and Nahm equations journal, October 1997

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Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups journal, November 2013

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A comment on the spectrum of H-monopoles journal, April 1997

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Gauge Noninvariance and Parity Nonconservation of Three-Dimensional Fermions journal, January 1984

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

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Framed BPS states journal, January 2013

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Fusion rules and modular transformations in 2D conformal field theory journal, January 1988

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Quantum Quivers and Hall/Hole Halos text, January 2002

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Framed BPS States preprint, January 2010

On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics journal, September 2018

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

D -Particle Bound States and Generalized Instantons journal, January 2000

Mirror symmetry in three dimensional gauge theories journal, October 1996

D-Brane Bound States Redux journal, June 1998

A topologically twisted index for three-dimensional supersymmetric theories journal, July 2015

D-particle bound states and generalized instantons text, January 1998

On the phase transition towards permanent quark confinement journal, June 1978

Electric-Magnetic Duality And The Geometric Langlands Program preprint, January 2006

Loop operators and S-duality from curves on Riemann surfaces text, January 2009

Gauge theory loop operators and Liouville theory journal, February 2010

Quantum Quivers and Hall/Hole Halos journal, October 2002

Witten index and wall crossing journal, January 2015

Chern-Simons theory and S-duality journal, May 2013

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops text, January 2007

Monopole bubbling via string theory journal, November 2018

Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces journal, July 1997

Loop operators and S-duality from curves on Riemann surfaces journal, September 2009

Liouville Correlation Functions from Four-dimensional Gauge Theories text, January 2009

Semiclassical framed BPS states journal, July 2016

Anomalous behaviour of the witten index-exactly soluble models journal, November 1984

Wall crossing from Dirac zeromodes journal, September 2018

Wall Crossing from Dirac Zeromodes text, January 2018

A topologically twisted index for three-dimensional supersymmetric theories text, January 2015

Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops journal, May 2012

Index-like theorems from line defect vevs journal, September 2019

Axial-Anomaly-Induced Fermion Fractionization and Effective Gauge-Theory Actions in Odd-Dimensional Space-Times journal, December 1983

A Comment on the Spectrum of H-Monopoles text, January 1996

Anomalous behaviour of the witten index-exactly soluble models journal, November 1984

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops text, January 2007

Loop and surface operators in N=2 gauge theory and Liouville modular geometry text, January 2009

ABCD of instantons text, January 2004

Comments on string dynamics in six dimensions
journal, July 1996

Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions
text, January 1997

N = 2 dualities
journal, August 2012

ABCD of Instantons
journal, September 2004

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories
journal, November 2014

Parameter counting for singular monopoles on ℝ3
journal, October 2014

Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
text, January 1997

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Witten Index and Threshold Bound States of D-Branes
text, January 1997

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010

D-branes, Monopoles and Nahm Equations
text, January 1996

Deconstructing (2,0) and Little String Theories
journal, January 2003

Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics
journal, May 1997

Anomalies and odd dimensions
journal, September 1985

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

The holographic dual of AdS 3 × S3 × S3 × S1
journal, April 2014

Rigid Supersymmetric Theories in Curved Superspace
text, January 2011

D-branes, monopoles and Nahm equations
journal, October 1997

Witten index and threshold bound states of D-branes
journal, November 1997

Electric-magnetic duality and the geometric Langlands program
journal, January 2007

Darboux coordinates, Yang-Yang functional, and gauge theory
journal, October 2014

Mirror Symmetry in Three Dimensional Gauge Theories
text, January 1996

General instanton counting and 5d SCFT
journal, July 2015

Branes, instantons, and Taub-NUT spaces
journal, June 2009

Singular monopoles and supersymmetric gauge theories in three dimensions
journal, August 1998

Brane bending and monopole moduli
journal, October 2014

Rigid supersymmetric theories in curved superspace
journal, June 2011

Exact results for ’t Hooft loops in Gauge theories on S 4
journal, May 2012

String theory of the Omega deformation
journal, January 2012

Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups
journal, November 2013

Yang-Mills instantons on ALE gravitational instantons
journal, December 1990

A comment on the spectrum of H-monopoles
journal, April 1997

Line operators on $ {S^{{1}}} \times {\mathbb{R}^{{3}}} $ and quantization of the Hitchin moduli space
journal, April 2012

Gauge Noninvariance and Parity Nonconservation of Three-Dimensional Fermions
journal, January 1984

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

Semiclassical framed BPS states
text, January 2015

Framed BPS states
journal, January 2013

Liouville Correlation Functions from Four-Dimensional Gauge Theories
journal, January 2010

Fusion rules and modular transformations in 2D conformal field theory
journal, January 1988

Branes, Instantons, And Taub-NUT Spaces
text, January 2009

Quantum Quivers and Hall/Hole Halos
text, January 2002

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

Framed BPS States
preprint, January 2010

On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics
journal, September 2018

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

D -Particle Bound States and Generalized Instantons
journal, January 2000

Mirror symmetry in three dimensional gauge theories
journal, October 1996

D-Brane Bound States Redux
journal, June 1998

A topologically twisted index for three-dimensional supersymmetric theories
journal, July 2015

D-particle bound states and generalized instantons
text, January 1998

On the phase transition towards permanent quark confinement
journal, June 1978

Electric-Magnetic Duality And The Geometric Langlands Program
preprint, January 2006

Loop operators and S-duality from curves on Riemann surfaces
text, January 2009

Gauge theory loop operators and Liouville theory
journal, February 2010

Quantum Quivers and Hall/Hole Halos
journal, October 2002

Witten index and wall crossing
journal, January 2015

Chern-Simons theory and S-duality
journal, May 2013

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
text, January 2007

Monopole bubbling via string theory
journal, November 2018

Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces
journal, July 1997

Loop operators and S-duality from curves on Riemann surfaces
journal, September 2009

Liouville Correlation Functions from Four-dimensional Gauge Theories
text, January 2009

Semiclassical framed BPS states
journal, July 2016

Anomalous behaviour of the witten index-exactly soluble models
journal, November 1984

Wall crossing from Dirac zeromodes
journal, September 2018

Wall Crossing from Dirac Zeromodes
text, January 2018

A topologically twisted index for three-dimensional supersymmetric theories
text, January 2015

Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
journal, May 2012

Index-like theorems from line defect vevs
journal, September 2019

Axial-Anomaly-Induced Fermion Fractionization and Effective Gauge-Theory Actions in Odd-Dimensional Space-Times
journal, December 1983

A Comment on the Spectrum of H-Monopoles
text, January 1996

Anomalous behaviour of the witten index-exactly soluble models
journal, November 1984

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
text, January 2007

Loop and surface operators in N=2 gauge theory and Liouville modular geometry
text, January 2009

ABCD of instantons
text, January 2004