Index-like theorems from line defect vevs

Brennan, T. Daniel; Moore, Gregory W.

doi:10.1007/jhep09(2019)073

Title: Index-like theorems from line defect vevs

Abstract

In this paper we investigate the relation between complexified Fenchel-Nielsen coordinates and spectral network coordinates on Seiberg-Witten moduli space. The main technique is the comparison of exact expressions for the expectation value of ’t Hooft defects in certain 4D SU(2) N = 2 gauge theories. We derive an index-like theorem for a class of Dirac operators on singular monopole moduli spaces. Our expression determines the indices of Dirac operators on singular monopole moduli spaces in terms of characteristic numbers for vector bundles over certain Kronheimer-Nakajima quiver varieties.

Authors:

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

Rutgers Univ., Piscataway, NJ (United States)

Publication Date:: 2019-09-10

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

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

OSTI Identifier:: 1611320

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: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Differential and Algebraic Geometry; Supersymmetric Gauge Theory; Wilson; ’t Hooft and Polyakov loops

Citation Formats


                    Brennan, T. Daniel, and Moore, Gregory W. Index-like theorems from line defect vevs.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep09(2019)073.

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                    Brennan, T. Daniel, & Moore, Gregory W. Index-like theorems from line defect vevs.  United States.  https://doi.org/10.1007/jhep09(2019)073

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                    Brennan, T. Daniel, and Moore, Gregory W. Tue .  
"Index-like theorems from line defect vevs".  United States.  https://doi.org/10.1007/jhep09(2019)073.  https://www.osti.gov/servlets/purl/1611320.

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@article{osti_1611320,

  title        = {Index-like theorems from line defect vevs},

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

  abstractNote = {In this paper we investigate the relation between complexified Fenchel-Nielsen coordinates and spectral network coordinates on Seiberg-Witten moduli space. The main technique is the comparison of exact expressions for the expectation value of ’t Hooft defects in certain 4D SU(2) N = 2 gauge theories. We derive an index-like theorem for a class of Dirac operators on singular monopole moduli spaces. Our expression determines the indices of Dirac operators on singular monopole moduli spaces in terms of characteristic numbers for vector bundles over certain Kronheimer-Nakajima quiver varieties.},

  doi          = {10.1007/jhep09(2019)073},

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

  number       = 9,

  volume       = 2019,

  place        = {United States},

  year         = {2019},

  month        = {9}

}

Copy to clipboard

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Works referenced in this record:

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Works referencing / citing this record:

’t Hooft defects and wall crossing in SQM
journal, October 2019

Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W.
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)173

't Hooft Defects and Wall Crossing in SQM
text, January 2018

Brennan, T. Daniel; Dey, Anindya; Moore, Gregory W.
arXiv
DOI: 10.48550/arxiv.1810.07191

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Title: Index-like theorems from line defect vevs

Abstract

Citation Formats

On monopole bubbling contributions to ’t Hooft loops journal, May 2019

N = 2 dualities journal, August 2012

Spectral Networks journal, March 2013

Spectral Networks and Snakes journal, March 2013

ADE spectral networks and decoupling limits of surface defects journal, February 2017

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Principal Moduli and Class Fields journal, December 2003

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

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

Solutions of four-dimensional field theories via M-theory journal, September 1997

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

Monopoles and Wilson lines journal, June 2014

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

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

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

Monopole bubbling via string theory journal, November 2018

A remark on the scattering of BPS monopoles journal, March 1982

Equivariant Volumes of Non-Compact Quotients and Instanton Counting journal, May 2008

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

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

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

ADE spectral networks journal, August 2016

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

Spectral Networks and Fenchel–Nielsen Coordinates journal, May 2016

Framed BPS states journal, January 2013

On the geometry and dynamics of diffeomorphisms of surfaces journal, April 1988

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

A note on the semiclassical formulation of BPS states in four-dimensional N=2 theories journal, December 2016

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

Gauge theory loop operators and Liouville theory journal, February 2010

Semiclassical framed BPS states journal, July 2016

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

Framed BPS States preprint, January 2010

Spectral networks text, January 2012

On Monopole Bubbling Contributions to 't Hooft Loops text, January 2019

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

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

Solutions Of Four-Dimensional Field Theories Via M Theory text, January 1997

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

Principal moduli and class fields preprint, January 2003

’t Hooft defects and wall crossing in SQM journal, October 2019

't Hooft Defects and Wall Crossing in SQM text, January 2018

On monopole bubbling contributions to ’t Hooft loops
journal, May 2019

N = 2 dualities
journal, August 2012

Spectral Networks
journal, March 2013

Spectral Networks and Snakes
journal, March 2013

ADE spectral networks and decoupling limits of surface defects
journal, February 2017

Bundles over Moduli Spaces and the Quantization of BPS Monopoles
journal, August 1993

Self-dual strings and N = 2 supersymmetric field theory
journal, October 1996

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Supersymmetric Boundary Conditions in $\mathcal{N}=4$ Super Yang-Mills Theory
journal, February 2009

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

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

Principal Moduli and Class Fields
journal, December 2003

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

Integrating over Higgs Branches
journal, January 2000

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

Solutions of four-dimensional field theories via M-theory
journal, September 1997

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

Monopoles and Wilson lines
journal, June 2014

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

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

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

Monopole bubbling via string theory
journal, November 2018

A remark on the scattering of BPS monopoles
journal, March 1982

Equivariant Volumes of Non-Compact Quotients and Instanton Counting
journal, May 2008

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

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

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

ADE spectral networks
journal, August 2016

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

Spectral Networks and Fenchel–Nielsen Coordinates
journal, May 2016

Framed BPS states
journal, January 2013

On the geometry and dynamics of diffeomorphisms of surfaces
journal, April 1988

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

A note on the semiclassical formulation of BPS states in four-dimensional N=2 theories
journal, December 2016

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

Gauge theory loop operators and Liouville theory
journal, February 2010

Semiclassical framed BPS states
journal, July 2016

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

Framed BPS States
preprint, January 2010

Spectral networks
text, January 2012

On Monopole Bubbling Contributions to 't Hooft Loops
text, January 2019

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

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

Solutions Of Four-Dimensional Field Theories Via M Theory
text, January 1997

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

Principal moduli and class fields
preprint, January 2003

’t Hooft defects and wall crossing in SQM
journal, October 2019

't Hooft Defects and Wall Crossing in SQM
text, January 2018