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Title: Exceptional Chern-Simons-Matter dualities

Abstract

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is (E_{N})_{1}\leftrightarrow SU(9-N)_{-1} ( E N ) 1 S U ( 9 N ) 1 . Others such as SO(3)_{8}\leftrightarrow PSU(3)_{-6}, S O ( 3 ) 8 P S U ( 3 ) 6 , are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons-matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant G_{2} G 2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

Authors:
 [1];  [2];  [1]
  1. Institute for Advanced Study, Princeton University
  2. Walter Burke Institute for Theoretical Physics
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1572130
Grant/Contract Number:  
SC0009988; SC0011632
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Cordova, Clay, Hsin, Po-Shen, and Ohmori, Kantaro. Exceptional Chern-Simons-Matter dualities. Netherlands: N. p., 2019. Web. doi:10.21468/SciPostPhys.7.4.056.
Cordova, Clay, Hsin, Po-Shen, & Ohmori, Kantaro. Exceptional Chern-Simons-Matter dualities. Netherlands. doi:10.21468/SciPostPhys.7.4.056.
Cordova, Clay, Hsin, Po-Shen, and Ohmori, Kantaro. Mon . "Exceptional Chern-Simons-Matter dualities". Netherlands. doi:10.21468/SciPostPhys.7.4.056.
@article{osti_1572130,
title = {Exceptional Chern-Simons-Matter dualities},
author = {Cordova, Clay and Hsin, Po-Shen and Ohmori, Kantaro},
abstractNote = {We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is (E_{N})_{1}\leftrightarrow SU(9-N)_{-1} ( E N ) 1 ↔ S U ( 9 − N ) − 1 . Others such as SO(3)_{8}\leftrightarrow PSU(3)_{-6}, S O ( 3 ) 8 ↔ P S U ( 3 ) − 6 , are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons-matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant G_{2} G 2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.},
doi = {10.21468/SciPostPhys.7.4.056},
journal = {SciPost Physics Proceedings},
number = 4,
volume = 7,
place = {Netherlands},
year = {2019},
month = {10}
}

Journal Article:
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DOI: 10.21468/SciPostPhys.7.4.056

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Works referenced in this record:

Eigenvalue inequalities for fermions in gauge theories
journal, September 1984

  • Vafa, Cumrun; Witten, Edward
  • Communications in Mathematical Physics, Vol. 95, Issue 3
  • DOI: 10.1007/BF01212397

On 2-group global symmetries and their anomalies
journal, March 2019

  • Benini, Francesco; Córdova, Clay; Hsin, Po-Shen
  • Journal of High Energy Physics, Vol. 2019, Issue 3
  • DOI: 10.1007/JHEP03(2019)118

Chern Simons duality with a fundamental boson and fermion
journal, November 2013

  • Jain, Sachin; Minwalla, Shiraz; Yokoyama, Shuichi
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)037

Bosonization and mirror symmetry
journal, October 2016


Conformal subalgebras of Kac-Moody algebras
journal, November 1986


Comments on one-form global symmetries and their gauging in 3d and 4d
journal, January 2019


Anomaly Indicators for Time-Reversal Symmetric Topological Orders
journal, September 2017


Baryons, monopoles and dualities in Chern-Simons-matter theories
journal, February 2016


A study of time reversal symmetry of abelian anyons
journal, July 2018


Parity Conservation in Quantum Chromodynamics
journal, August 1984


Extremal transitions and five-dimensional supersymmetric field theories
journal, January 1997


Dual Dirac Liquid on the Surface of the Electron Topological Insulator
journal, November 2015


Generalized global symmetries
journal, February 2015

  • Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)172

Fermion path integrals and topological phases
journal, July 2016


Level-rank duality of the U( N ) WZW model, Chern-Simons theory, and 2d qYM theory
journal, June 2007


Holographic aspects of three dimensional QCD from string theory
journal, May 2010


Curious aspects of three-dimensional N = 1 $$ \mathcal{N}=1 $$ SCFTs
journal, August 2018

  • Gaiotto, Davide; Komargodski, Zohar; Wu, Jingxiang
  • Journal of High Energy Physics, Vol. 2018, Issue 8
  • DOI: 10.1007/JHEP08(2018)004

Decompositions of representations of exceptional affine algebras with respect to conformal subalgebras
journal, April 1988


Time-reversal symmetry, anomalies, and dualities in (2+1)$d$
journal, January 2018


Phases Of Adjoint QCD$_3$ And Dualities
journal, January 2018


Group-level duality in WZW models and Chern-Simons theory
journal, August 1990


Chern–Simons theory with vector fermion matter
journal, August 2012


Phases of N = 1 $$ \mathcal{N}=1 $$ theories in 2 + 1 dimensions
journal, July 2018

  • Bashmakov, Vladimir; Gomis, Jaume; Komargodski, Zohar
  • Journal of High Energy Physics, Vol. 2018, Issue 7
  • DOI: 10.1007/JHEP07(2018)123

Naturality in conformal field theory
journal, January 1989


Conformal embeddings, rank-level duality and exceptional modular invariants
journal, April 1991

  • Verstegen, D.
  • Communications in Mathematical Physics, Vol. 137, Issue 3
  • DOI: 10.1007/BF02100278

Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions
journal, December 2012

  • Aharony, Ofer; Gur-Ari, Guy; Yacoby, Ran
  • Journal of High Energy Physics, Vol. 2012, Issue 12
  • DOI: 10.1007/JHEP12(2012)028

Anyons in an exactly solved model and beyond
journal, January 2006


Conformal Embeddings and Simple Current Extensions
journal, June 2014

  • Kac, Victor G.; Frajria, Pierluigi Möseneder; Papi, Paolo
  • International Mathematics Research Notices, Vol. 2015, Issue 14
  • DOI: 10.1093/imrn/rnu092

Dualities and phases of 3d N = 1 $$ \mathcal{N}=1 $$ SQCD
journal, October 2018

  • Choi, Changha; Roček, Martin; Sharon, Adar
  • Journal of High Energy Physics, Vol. 2018, Issue 10
  • DOI: 10.1007/JHEP10(2018)105

A symmetry breaking scenario for QCD3
journal, January 2018

  • Komargodski, Zohar; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2018, Issue 1
  • DOI: 10.1007/JHEP01(2018)109

Strange Duality for Verlinde Spaces of Exceptional Groups at Level One
journal, September 2009


N $$ \mathcal{N} $$ = 1 dualities in 2+1 dimensions
journal, November 2018

  • Benini, Francesco; Benvenuti, Sergio
  • Journal of High Energy Physics, Vol. 2018, Issue 11
  • DOI: 10.1007/JHEP11(2018)197

Assembling Fibonacci anyons from a Z 3 parafermion lattice model
journal, June 2015


Five dimensional SUSY field theories, non-trivial fixed points and string dynamics
journal, November 1996


Restrictions on symmetry breaking in vector-like gauge theories
journal, March 1984


Spin module versions of Weyl's reciprocity theorem for classical Kac-Moody Lie algebras---an application to branching rule duality
journal, January 1989

  • Hasegawa, Koji
  • Publications of the Research Institute for Mathematical Sciences, Vol. 25, Issue 5
  • DOI: 10.2977/prims/1195172705

Group-level duality of WZW fusion coefficients and Chern-Simons link observables
journal, April 1991


d = 3 bosonic vector models coupled to Chern-Simons gauge theories
journal, March 2012

  • Aharony, Ofer; Gur-Ari, Guy; Yacoby, Ran
  • Journal of High Energy Physics, Vol. 2012, Issue 3
  • DOI: 10.1007/JHEP03(2012)037

A duality web in 2 + 1 dimensions and condensed matter physics
journal, November 2016


Three dimensional bosonization from supersymmetry
journal, November 2015


Level/rank duality and Chern-Simons-matter theories
journal, September 2016


Interacting Anyons in Topological Quantum Liquids: The Golden Chain
journal, April 2007


Non-Abelian anyons and topological quantum computation
journal, September 2008


Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model
journal, November 2013


Interacting fermionic topological insulators/superconductors in three dimensions
journal, May 2014


Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
journal, January 2018


Taming the conformal zoo
journal, April 1989


Phase Transition in a Lattice Model of Superconductivity
journal, November 1981


Three-dimensional dualities with bosons and fermions
journal, February 2018


Particle-Vortex Duality from 3D Bosonization
journal, September 2016


Mandelstam-'t Hooft duality in abelian lattice models
journal, July 1978


Level-rank duality of WZW models in conformal field theory
journal, February 1992

  • Nakanishi, Tomoki; Tsuchiya, Akihiro
  • Communications in Mathematical Physics, Vol. 144, Issue 2
  • DOI: 10.1007/BF02101097

Time-reversal and spatial-reflection symmetry localization anomalies in (2+1)-dimensional topological phases of matter
journal, September 2018


Chern-Simons-matter dualities with SO and USp gauge groups
journal, February 2017

  • Aharony, Ofer; Benini, Francesco; Hsin, Po-Shen
  • Journal of High Energy Physics, Vol. 2017, Issue 2
  • DOI: 10.1007/JHEP02(2017)072

Exploring 2-group global symmetries
journal, February 2019

  • Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
  • Journal of High Energy Physics, Vol. 2019, Issue 2
  • DOI: 10.1007/JHEP02(2019)184