Argyres-Douglas theories, chiral algebras and wild Hitchin characters

doi:10.1007/jhep01(2018)150

Title: Argyres-Douglas theories, chiral algebras and wild Hitchin characters

Abstract

We use Coulomb branch indices of Argyres-Douglas theories on S¹ × L(k,1) to quantize moduli spaces $$\mathcal{M}$$_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the “wild Hitchin characters” — the graded dimensions of the Hilbert spaces from quantization — for four infinite families of $$\mathcal{M}$$_H , giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in $$\mathcal{M}$$_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform ST^kS in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

Authors:

Fredrickson, Laura ^[1]; Pei, Du ^[2]; Yan, Wenbin ^[3]; Ye, Ke ^[4]

Stanford Univ., CA (United States)
California Inst. of Tech., Pasadena (United States); Univ. of Aarhus, Aarhus (Denmark)
Tsinghua Univ., Beijing (China); Harvard Univ., Cambridge, MA (United States)
California Inst. of Tech., Pasadena (United States)

Publication Date:: 2018-01-20

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1499648

Grant/Contract Number:: SC0011632

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: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Differential and Algebraic Geometry; Supersymmetry and Duality

Citation Formats


                    Fredrickson, Laura, Pei, Du, Yan, Wenbin, and Ye, Ke. Argyres-Douglas theories, chiral algebras and wild Hitchin characters.  United States: N. p., 2018. 
        Web.  doi:10.1007/jhep01(2018)150.

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                    Fredrickson, Laura, Pei, Du, Yan, Wenbin, & Ye, Ke. Argyres-Douglas theories, chiral algebras and wild Hitchin characters.  United States.  doi:10.1007/jhep01(2018)150.

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                    Fredrickson, Laura, Pei, Du, Yan, Wenbin, and Ye, Ke. Sat .  
        "Argyres-Douglas theories, chiral algebras and wild Hitchin characters".  United States.  doi:10.1007/jhep01(2018)150.  https://www.osti.gov/servlets/purl/1499648.

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@article{osti_1499648,

  title        = {Argyres-Douglas theories, chiral algebras and wild Hitchin characters},

  author       = {Fredrickson, Laura and Pei, Du and Yan, Wenbin and Ye, Ke},

  abstractNote = {We use Coulomb branch indices of Argyres-Douglas theories on S1 × L(k,1) to quantize moduli spaces $\mathcal{M}$H of wild/irregular Hitchin systems. In particular, we obtain formulae for the “wild Hitchin characters” — the graded dimensions of the Hilbert spaces from quantization — for four infinite families of $\mathcal{M}$H , giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in $\mathcal{M}$H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform STkS in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.},

  doi          = {10.1007/jhep01(2018)150},

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

  number       = 1,

  volume       = 2018,

  place        = {United States},

  year         = {2018},

  month        = {1}

}

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DOI: 10.1007/jhep01(2018)150

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Title: Argyres-Douglas theories, chiral algebras and wild Hitchin characters

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Constraints on chiral operators in N = 2 $$ \mathcal{N}=2 $$ SCFTs journal, December 2014

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Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories journal, December 2012

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Quantum reduction and representation theory of superconformal algebras journal, July 2004

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Quantum Higgs branches of isolated $\mathcal{N}=2$ superconformal field theories journal, October 2012

Higher S-dualities and Shephard-Todd groups journal, September 2015

Wild non-abelian Hodge theory on curves journal, January 2004

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Comments on scaling limits of 4d $ \mathcal{N} = 2 $ theories journal, January 2011

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Modular data and Verlinde formulae for fractional level WZW models I journal, December 2012

Higgs branch localization of N $$ \mathcal{N} $$ = 1 theories on S 3 × S 1 journal, August 2014

Stable bundles and integrable systems journal, January 1987

Study of N = 2 superconformal field theories in 4 dimensions journal, July 1996

New phenomena in SU(3) supersymmetric gauge theory journal, August 1995

Harmonic metrics and connections with irregular singularities journal, January 1999

Mirrors of 3d Sicilian theories journal, September 2010

Mirror symmetry, Langlands duality, and the Hitchin system journal, July 2003

On Braiding and Dyslexia journal, January 1995

Twisted Harmonic Maps and the Self-Duality Equations journal, July 1987

Branes and quantization journal, January 2009

Integrating over Higgs Branches journal, January 2000

Infrared computations of defect Schur indices journal, November 2016

Modular data and Verlinde formulae for fractional level WZW models II journal, October 2013

Chiral algebras for trinion theories journal, February 2015

Fivebranes and 3-manifold homology journal, July 2017

Tinkertoys for Gaiotto duality journal, November 2010

The Betti Numbers of the Moduli Space of Stable rank 3 Higgs Bundles on a Riemann Surface journal, December 1994

Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index journal, April 2017

Down the rabbit hole with theories of class S $$ \mathcal{S} $$ journal, October 2014

Fusion categories arising from semisimple Lie algebras journal, May 1995

New = 2 superconformal field theories in four dimensions journal, February 1996

NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES journal, February 2013

On a modular property of $ \mathcal{N}=2 $ superconformal theories in four dimensions journal, October 2012

Chiral algebras of class S $$ \mathcal{S} $$ journal, May 2015

N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations journal, December 2016

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs journal, February 2017

Equivariant Verlinde Formula from Fivebranes and Vortices journal, July 2017

Global Properties of Supersymmetric Theories and the Lens Space journal, July 2014

Schur correlation functions on S3 × S1 journal, July 2019

Schur correlation functions on S3 × S1 journal, July 2019

On the chiral algebra of Argyres-Douglas theories and S-duality journal, April 2018

Notes on integral identities for 3d supersymmetric dualities journal, April 2018

Four-dimensional lens space index from two-dimensional chiral algebra journal, July 2018

Vertex operator algebras, Higgs branches, and modular differential equations journal, August 2018

Logarithmic W-algebras and Argyres-Douglas theories at higher rank journal, November 2018

VOA[ M 4 ] journal, January 2020

Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6D (2,0) theories journal, July 2019

The conformal bootstrap: Theory, numerical techniques, and applications journal, January 2019

N = 2 dualities
journal, August 2012

Superconformal fixed points with En global symmetry
journal, March 1997

Wild quiver gauge theories
journal, February 2012

Constraints on chiral operators in N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, December 2014

An N = 2 superconformal fixed point with E6 global symmetry
journal, December 1996

Topological reduction of 4D SYM to 2D σ-models
journal, August 1995

Central charges and U(1) _R symmetries in Script N = 1 super Yang-Mills
journal, November 2003

Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
journal, July 1988

Hitchin equation, singularity, and N = 2 superconformal field theories
journal, March 2010

Gauge Theories and Macdonald Polynomials
journal, November 2012

Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
journal, February 2016

The Self-Duality Equations on a Riemann Surface
journal, July 1987

Schur indices, BPS particles, and Argyres-Douglas theories
journal, January 2016

Through the analytic halo: Fission via irregular singularities
journal, January 2009

More three dimensional mirror pairs
journal, May 2011

Coset Constructions of Logarithmic (1, p) Models
journal, January 2014

Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories
journal, December 2012

On S-duality of the superconformal index on lens spaces and 2d TQFT
journal, May 2013

The exact superconformal R-symmetry maximizes a
journal, September 2003

Elliptic hypergeometric integrals and ’t Hooft anomaly matching conditions
journal, June 2012

Asymptotically free = 2 theories and irregular conformal blocks
journal, December 2013

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

Factorisation and holomorphic blocks in 4d
journal, November 2015

Quantum reduction and representation theory of superconformal algebras
journal, July 2004

Twisted Modules for Vertex Algebras Associated with Even Lattices
journal, April 1994

Painlevé functions of the third kind
journal, May 1977

Quantum Higgs branches of isolated $\mathcal{N}=2$ superconformal field theories
journal, October 2012

Higher S-dualities and Shephard-Todd groups
journal, September 2015

Wild non-abelian Hodge theory on curves
journal, January 2004

S-duality and the $ \mathcal{N}=2 $ lens space index
journal, October 2013

Comments on scaling limits of 4d $ \mathcal{N} = 2 $ theories
journal, January 2011

Argyres-Douglas theories and S-duality
journal, February 2015

General Argyres-Douglas theory
journal, January 2013

Flat $G$-bundles with canonical metrics
journal, January 1988

Infinite Chiral Symmetry in Four Dimensions
journal, January 2015

Modular data and Verlinde formulae for fractional level WZW models I
journal, December 2012

Higgs branch localization of N $$ \mathcal{N} $$ = 1 theories on S 3 × S 1
journal, August 2014

Stable bundles and integrable systems
journal, January 1987

Study of N = 2 superconformal field theories in 4 dimensions
journal, July 1996

New phenomena in SU(3) supersymmetric gauge theory
journal, August 1995

Harmonic metrics and connections with irregular singularities
journal, January 1999

Mirrors of 3d Sicilian theories
journal, September 2010

Mirror symmetry, Langlands duality, and the Hitchin system
journal, July 2003

On Braiding and Dyslexia
journal, January 1995

Twisted Harmonic Maps and the Self-Duality Equations
journal, July 1987

Branes and quantization
journal, January 2009

Integrating over Higgs Branches
journal, January 2000

Infrared computations of defect Schur indices
journal, November 2016

Modular data and Verlinde formulae for fractional level WZW models II
journal, October 2013

Chiral algebras for trinion theories
journal, February 2015

Fivebranes and 3-manifold homology
journal, July 2017

Tinkertoys for Gaiotto duality
journal, November 2010

The Betti Numbers of the Moduli Space of Stable rank 3 Higgs Bundles on a Riemann Surface
journal, December 1994

Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
journal, April 2017

Down the rabbit hole with theories of class S $$ \mathcal{S} $$
journal, October 2014

Fusion categories arising from semisimple Lie algebras
journal, May 1995

New = 2 superconformal field theories in four dimensions
journal, February 1996

NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES
journal, February 2013

On a modular property of $ \mathcal{N}=2 $ superconformal theories in four dimensions
journal, October 2012

Chiral algebras of class S $$ \mathcal{S} $$
journal, May 2015

N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations
journal, December 2016

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, February 2017

Equivariant Verlinde Formula from Fivebranes and Vortices
journal, July 2017

Global Properties of Supersymmetric Theories and the Lens Space
journal, July 2014

Schur correlation functions on S3 × S1
journal, July 2019

Schur correlation functions on S3 × S1
journal, July 2019

On the chiral algebra of Argyres-Douglas theories and S-duality
journal, April 2018

Notes on integral identities for 3d supersymmetric dualities
journal, April 2018

Four-dimensional lens space index from two-dimensional chiral algebra
journal, July 2018

Vertex operator algebras, Higgs branches, and modular differential equations
journal, August 2018

Logarithmic W-algebras and Argyres-Douglas theories at higher rank
journal, November 2018

VOA[ M ₄ ]
journal, January 2020

Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6D (2,0) theories
journal, July 2019

The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019