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 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.
- Authors:
-
- 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:
- 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.
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.
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.
@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}
}
Web of Science
Works referenced in this record:
N = 2 dualities
journal, August 2012
- Gaiotto, Davide
- Journal of High Energy Physics, Vol. 2012, Issue 8
Superconformal fixed points with En global symmetry
journal, March 1997
- Minahan, Joseph A.; Nemeschansky, Dennis
- Nuclear Physics B, Vol. 489, Issue 1-2
Wild quiver gauge theories
journal, February 2012
- Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro
- Journal of High Energy Physics, Vol. 2012, Issue 2
Constraints on chiral operators in N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, December 2014
- Buican, Matthew; Nishinaka, Takahiro; Papageorgakis, Constantinos
- Journal of High Energy Physics, Vol. 2014, Issue 12
An N = 2 superconformal fixed point with E6 global symmetry
journal, December 1996
- Minahan, Joseph A.; Nemeschansku, Dennis
- Nuclear Physics B, Vol. 482, Issue 1-2
Topological reduction of 4D SYM to 2D σ-models
journal, August 1995
- Bershadsky, M.; Johansen, A.; Sadov, V.
- Nuclear Physics B, Vol. 448, Issue 1-2
Central charges and U(1) R symmetries in Script N = 1 super Yang-Mills
journal, November 2003
- Kutasov, David; Parnachev, Andrei; Sahakyan, David A.
- Journal of High Energy Physics, Vol. 2003, Issue 11
Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
journal, July 1988
- Kac, V. G.; Wakimoto, M.
- Proceedings of the National Academy of Sciences, Vol. 85, Issue 14
Hitchin equation, singularity, and N = 2 superconformal field theories
journal, March 2010
- Nanopoulos, Dimitri; Xie, Dan
- Journal of High Energy Physics, Vol. 2010, Issue 3
Gauge Theories and Macdonald Polynomials
journal, November 2012
- Gadde, Abhijit; Rastelli, Leonardo; Razamat, Shlomo S.
- Communications in Mathematical Physics, Vol. 319, Issue 1
Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
journal, February 2016
- Song, Jaewon
- Journal of High Energy Physics, Vol. 2016, Issue 2
The Self-Duality Equations on a Riemann Surface
journal, July 1987
- Hitchin, N. J.
- Proceedings of the London Mathematical Society, Vol. s3-55, Issue 1
Schur indices, BPS particles, and Argyres-Douglas theories
journal, January 2016
- Córdova, Clay; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2016, Issue 1
Through the analytic halo: Fission via irregular singularities
journal, January 2009
- Boalch, Philip
- Annales de l’institut Fourier, Vol. 59, Issue 7
More three dimensional mirror pairs
journal, May 2011
- Nanopoulos, Dimitri; Xie, Dan
- Journal of High Energy Physics, Vol. 2011, Issue 5
Coset Constructions of Logarithmic (1, p) Models
journal, January 2014
- Creutzig, Thomas; Ridout, David; Wood, Simon
- Letters in Mathematical Physics, Vol. 104, Issue 5
Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories
journal, December 2012
- Gaiotto, D.; Teschner, J.
- Journal of High Energy Physics, Vol. 2012, Issue 12
On S-duality of the superconformal index on lens spaces and 2d TQFT
journal, May 2013
- Alday, Luis F.; Bullimore, Mathew; Fluder, Martin
- Journal of High Energy Physics, Vol. 2013, Issue 5
The exact superconformal R-symmetry maximizes a
journal, September 2003
- Intriligator, Ken; Wecht, Brian
- Nuclear Physics B, Vol. 667, Issue 1-2
Elliptic hypergeometric integrals and ’t Hooft anomaly matching conditions
journal, June 2012
- Spiridonov, V. P.; Vartanov, G. S.
- Journal of High Energy Physics, Vol. 2012, Issue 6
Asymptotically free = 2 theories and irregular conformal blocks
journal, December 2013
- Gaiotto, Davide
- Journal of Physics: Conference Series, Vol. 462
Electric-magnetic duality and the geometric Langlands program
journal, January 2007
- Kapustin, Anton; Witten, Edward
- Communications in Number Theory and Physics, Vol. 1, Issue 1
Factorisation and holomorphic blocks in 4d
journal, November 2015
- Nieri, Fabrizio; Pasquetti, Sara
- Journal of High Energy Physics, Vol. 2015, Issue 11
Quantum reduction and representation theory of superconformal algebras
journal, July 2004
- Kac, Victor G.; Wakimoto, Minoru
- Advances in Mathematics, Vol. 185, Issue 2
Twisted Modules for Vertex Algebras Associated with Even Lattices
journal, April 1994
- Dong, C. Y.
- Journal of Algebra, Vol. 165, Issue 1
Painlevé functions of the third kind
journal, May 1977
- McCoy, Barry M.; Tracy, Craig A.; Wu, Tai Tsun
- Journal of Mathematical Physics, Vol. 18, Issue 5
Quantum Higgs branches of isolated $\mathcal{N}=2$ superconformal field theories
journal, October 2012
- Argyres, Philip C.; Maruyoshi, Kazunobu; Tachikawa, Yuji
- Journal of High Energy Physics, Vol. 2012, Issue 10
Higher S-dualities and Shephard-Todd groups
journal, September 2015
- Cecotti, Sergio; Del Zotto, Michele
- Journal of High Energy Physics, Vol. 2015, Issue 9
Wild non-abelian Hodge theory on curves
journal, January 2004
- Biquard, Olivier; Boalch, Philip
- Compositio Mathematica, Vol. 140, Issue 01
S-duality and the $ \mathcal{N}=2 $ lens space index
journal, October 2013
- Razamat, Shlomo S.; Yamazaki, Masahito
- Journal of High Energy Physics, Vol. 2013, Issue 10
Comments on scaling limits of 4d $ \mathcal{N} = 2 $ theories
journal, January 2011
- Gaiotto, Davide; Seiberg, Nathan; Tachikawa, Yuji
- Journal of High Energy Physics, Vol. 2011, Issue 1
Argyres-Douglas theories and S-duality
journal, February 2015
- Buican, Matthew; Giacomelli, Simone; Nishinaka, Takahiro
- Journal of High Energy Physics, Vol. 2015, Issue 2
General Argyres-Douglas theory
journal, January 2013
- Xie, Dan
- Journal of High Energy Physics, Vol. 2013, Issue 1
Flat $G$-bundles with canonical metrics
journal, January 1988
- Corlette, Kevin
- Journal of Differential Geometry, Vol. 28, Issue 3
Infinite Chiral Symmetry in Four Dimensions
journal, January 2015
- Beem, Christopher; Lemos, Madalena; Liendo, Pedro
- Communications in Mathematical Physics, Vol. 336, Issue 3
Modular data and Verlinde formulae for fractional level WZW models I
journal, December 2012
- Creutzig, Thomas; Ridout, David
- Nuclear Physics B, Vol. 865, Issue 1
Higgs branch localization of N $$ \mathcal{N} $$ = 1 theories on S 3 × S 1
journal, August 2014
- Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2014, Issue 8
Stable bundles and integrable systems
journal, January 1987
- Hitchin, Nigel
- Duke Mathematical Journal, Vol. 54, Issue 1
Study of N = 2 superconformal field theories in 4 dimensions
journal, July 1996
- Eguchi, Tohru; Hori, Kentaro; Ito, Katsushi
- Nuclear Physics B, Vol. 471, Issue 3
New phenomena in SU(3) supersymmetric gauge theory
journal, August 1995
- Argyres, Philip C.; Douglas, Michael R.
- Nuclear Physics B, Vol. 448, Issue 1-2
Harmonic metrics and connections with irregular singularities
journal, January 1999
- Sabbah, Claude
- Annales de l’institut Fourier, Vol. 49, Issue 4
Mirrors of 3d Sicilian theories
journal, September 2010
- Benini, Francesco; Tachikawa, Yuji; Xie, Dan
- Journal of High Energy Physics, Vol. 2010, Issue 9
Mirror symmetry, Langlands duality, and the Hitchin system
journal, July 2003
- Hausel, Tam�s; Thaddeus, Michael
- Inventiones Mathematicae, Vol. 153, Issue 1
Twisted Harmonic Maps and the Self-Duality Equations
journal, July 1987
- Donaldson, S. K.
- Proceedings of the London Mathematical Society, Vol. s3-55, Issue 1
Branes and quantization
journal, January 2009
- Gukov, Sergei; Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 13, Issue 5
Integrating over Higgs Branches
journal, January 2000
- Moore, Gregory; Nekrasov, Nikita; Shatashvili, Samson
- Communications in Mathematical Physics, Vol. 209, Issue 1
Infrared computations of defect Schur indices
journal, November 2016
- Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng
- Journal of High Energy Physics, Vol. 2016, Issue 11
Modular data and Verlinde formulae for fractional level WZW models II
journal, October 2013
- Creutzig, Thomas; Ridout, David
- Nuclear Physics B, Vol. 875, Issue 2
Chiral algebras for trinion theories
journal, February 2015
- Lemos, Madalena; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2015, Issue 2
Fivebranes and 3-manifold homology
journal, July 2017
- Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun
- Journal of High Energy Physics, Vol. 2017, Issue 7
Tinkertoys for Gaiotto duality
journal, November 2010
- Chacaltana, Oscar; Distler, Jacques
- Journal of High Energy Physics, Vol. 2010, Issue 11
The Betti Numbers of the Moduli Space of Stable rank 3 Higgs Bundles on a Riemann Surface
journal, December 1994
- Gothen, Peter B.
- International Journal of Mathematics, Vol. 05, Issue 06
Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
journal, April 2017
- Maruyoshi, Kazunobu; Song, Jaewon
- Physical Review Letters, Vol. 118, Issue 15
Down the rabbit hole with theories of class S $$ \mathcal{S} $$
journal, October 2014
- Razamat, Shlomo S.; Willett, Brian
- Journal of High Energy Physics, Vol. 2014, Issue 10
Fusion categories arising from semisimple Lie algebras
journal, May 1995
- Haahr Andersen, Henning; Paradowski, Jan
- Communications in Mathematical Physics, Vol. 169, Issue 3
New = 2 superconformal field theories in four dimensions
journal, February 1996
- Argyres, Philip C.; Ronen Plesser, M.; Seiberg, Nathan
- Nuclear Physics B, Vol. 461, Issue 1-2
NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES
journal, February 2013
- Chacaltana, Oscar; Distler, Jacques; Tachikawa, Yuji
- International Journal of Modern Physics A, Vol. 28, Issue 03n04
On a modular property of $ \mathcal{N}=2 $ superconformal theories in four dimensions
journal, October 2012
- Razamat, Shlomo S.
- Journal of High Energy Physics, Vol. 2012, Issue 10
Chiral algebras of class S $$ \mathcal{S} $$
journal, May 2015
- Beem, Christopher; Peelaers, Wolfger; Rastelli, Leonardo
- Journal of High Energy Physics, Vol. 2015, Issue 5
N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations
journal, December 2016
- Agarwal, Prarit; Maruyoshi, Kazunobu; Song, Jaewon
- Journal of High Energy Physics, Vol. 2016, Issue 12
N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs
journal, February 2017
- Maruyoshi, Kazunobu; Song, Jaewon
- Journal of High Energy Physics, Vol. 2017, Issue 2
Equivariant Verlinde Formula from Fivebranes and Vortices
journal, July 2017
- Gukov, Sergei; Pei, Du
- Communications in Mathematical Physics, Vol. 355, Issue 1
Global Properties of Supersymmetric Theories and the Lens Space
journal, July 2014
- Razamat, Shlomo S.; Willett, Brian
- Communications in Mathematical Physics, Vol. 334, Issue 2
Works referencing / citing this record:
Schur correlation functions on S3 × S1
journal, July 2019
- Pan, Yiwen; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2019, Issue 7
Schur correlation functions on S3 × S1
journal, July 2019
- Pan, Yiwen; Peelaers, Wolfger
- Journal of High Energy Physics, Vol. 2019, Issue 7
On the chiral algebra of Argyres-Douglas theories and S-duality
journal, April 2018
- Choi, Jaewang; Nishinaka, Takahiro
- Journal of High Energy Physics, Vol. 2018, Issue 4
Notes on integral identities for 3d supersymmetric dualities
journal, April 2018
- Aghaei, Nezhla; Amariti, Antonio; Sekiguchi, Yuta
- Journal of High Energy Physics, Vol. 2018, Issue 4
Four-dimensional lens space index from two-dimensional chiral algebra
journal, July 2018
- Fluder, Martin; Song, Jaewon
- Journal of High Energy Physics, Vol. 2018, Issue 7
Vertex operator algebras, Higgs branches, and modular differential equations
journal, August 2018
- Beem, Christopher; Rastelli, Leonardo
- Journal of High Energy Physics, Vol. 2018, Issue 8
Logarithmic W-algebras and Argyres-Douglas theories at higher rank
journal, November 2018
- Creutzig, Thomas
- Journal of High Energy Physics, Vol. 2018, Issue 11
VOA[ M 4 ]
journal, January 2020
- Feigin, Boris; Gukov, Sergei
- Journal of Mathematical Physics, Vol. 61, Issue 1
Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6D (2,0) theories
journal, July 2019
- Wang, Yifan; Xie, Dan
- Physical Review D, Vol. 100, Issue 2
The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019
- Poland, David; Rychkov, Slava; Vichi, Alessandro
- Reviews of Modern Physics, Vol. 91, Issue 1