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Title: Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

Abstract

We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete \theta θ -parameters, which control the weights in the sum over topologically distinct gauge bundles. We derive level-rank duality for these topological field theories. Our results may also be viewed as level-rank duality for SO(N)_{K} S O ( N ) K Chern-Simons theory in the presence of background fields for discrete global symmetries. In particular, we include the required counterterms and analysis of the anomalies. We couple our theories to charged matter and determine how these counterterms are shifted by integrating out massive fermions. By gauging discrete global symmetries we derive new boson-fermion dualities for vector matter, and present the phase diagram of theories with two-index tensor fermions, thus extending previous results for SO(N) S O ( N ) to other global forms of the gauge group.

Authors:
 [1];  [2];  [1]
  1. Institute for Advanced Study, Princeton University
  2. Princeton University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1435362
Grant/Contract Number:  
SC0009988
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 4 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 Seiberg, Nathan. Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups. Netherlands: N. p., 2018. Web. doi:10.21468/SciPostPhys.4.4.021.
Cordova, Clay, Hsin, Po-Shen, & Seiberg, Nathan. Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups. Netherlands. doi:10.21468/SciPostPhys.4.4.021.
Cordova, Clay, Hsin, Po-Shen, and Seiberg, Nathan. Sun . "Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups". Netherlands. doi:10.21468/SciPostPhys.4.4.021.
@article{osti_1435362,
title = {Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups},
author = {Cordova, Clay and Hsin, Po-Shen and Seiberg, Nathan},
abstractNote = {We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete \theta θ -parameters, which control the weights in the sum over topologically distinct gauge bundles. We derive level-rank duality for these topological field theories. Our results may also be viewed as level-rank duality for SO(N)_{K} S O ( N ) K Chern-Simons theory in the presence of background fields for discrete global symmetries. In particular, we include the required counterterms and analysis of the anomalies. We couple our theories to charged matter and determine how these counterterms are shifted by integrating out massive fermions. By gauging discrete global symmetries we derive new boson-fermion dualities for vector matter, and present the phase diagram of theories with two-index tensor fermions, thus extending previous results for SO(N) S O ( N ) to other global forms of the gauge group.},
doi = {10.21468/SciPostPhys.4.4.021},
journal = {SciPost Physics Proceedings},
number = 4,
volume = 4,
place = {Netherlands},
year = {2018},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.4.4.021

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Cited by: 26 works
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Works referenced in this record:

3d dualities from 4d dualities
journal, July 2013

  • Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2013, Issue 7
  • DOI: 10.1007/JHEP07(2013)149

Fermionic SPT phases in higher dimensions and bosonization
journal, October 2017

  • Kapustin, Anton; Thorngren, Ryan
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)080

Theta, time reversal and temperature
journal, May 2017

  • Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)091

Universal coverings of orthogonal groups
journal, March 2004


D-brane charges in five-brane backgrounds
journal, October 2001


Symmetry protected topological orders and the group cohomology of their symmetry group
journal, April 2013


Symmetries and strings in field theory and gravity
journal, April 2011


The Outer-Automorphic WZW Orbifolds on (2 n ), including Five Triality Orbifolds on (8)
journal, December 2002


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

A time-reversal invariant topological phase at the surface of a 3D topological insulator
journal, September 2013

  • Bonderson, Parsa; Nayak, Chetan; Qi, Xiao-Liang
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 09
  • DOI: 10.1088/1742-5468/2013/09/P09016

Duality and bosonization of ( 2 + 1 ) -dimensional Majorana fermions
journal, May 2017


Effect of interactions on two-dimensional fermionic symmetry-protected topological phases with Z 2 symmetry
journal, May 2014


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


Setting the Quantum Integrand of M-Theory
journal, January 2006

  • Freed, Daniel S.; Moore, Gregory W.
  • Communications in Mathematical Physics, Vol. 263, Issue 1
  • DOI: 10.1007/s00220-005-1482-7

The pin Groups in Physics: c, p and t
journal, August 2001

  • Berg, Marcus; DeWITT-MORETTE, CÉCile; Gwo, Shangjr
  • Reviews in Mathematical Physics, Vol. 13, Issue 08
  • DOI: 10.1142/S0129055X01000922

The Sum Over Topological Sectors and θ in the 2+1-Dimensional $${\mathbb{CP}^1 \sigma}$$ CP 1 σ -Model
journal, January 2018

  • Freed, Daniel S.; Komargodski, Zohar; Seiberg, Nathan
  • Communications in Mathematical Physics, Vol. 362, Issue 1
  • DOI: 10.1007/s00220-018-3093-0

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


Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories
journal, October 2012

  • Closset, Cyril; Dumitrescu, Thomas T.; Festuccia, Guido
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)053

Comments on Chern-Simons contact terms in three dimensions
journal, September 2012

  • Closset, Cyril; Dumitrescu, Thomas T.; Festuccia, Guido
  • Journal of High Energy Physics, Vol. 2012, Issue 9
  • DOI: 10.1007/JHEP09(2012)091

Coupling a QFT to a TQFT and duality
journal, April 2014


Fermionic symmetry protected topological phases and cobordisms
journal, December 2015

  • Kapustin, Anton; Thorngren, Ryan; Turzillo, Alex
  • Journal of High Energy Physics, Vol. 2015, Issue 12
  • DOI: 10.1007/JHEP12(2015)052

Gapped boundary phases of topological insulators via weak coupling
journal, November 2016

  • Seiberg, Nathan; Witten, Edward
  • Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12
  • DOI: 10.1093/ptep/ptw083

Topological gauge theories and group cohomology
journal, April 1990

  • Dijkgraaf, Robbert; Witten, Edward
  • Communications in Mathematical Physics, Vol. 129, Issue 2
  • DOI: 10.1007/BF02096988

Nonabelions in the fractional quantum hall effect
journal, August 1991


Reading between the lines of four-dimensional gauge theories
journal, August 2013

  • Aharony, Ofer; Seiberg, Nathan; Tachikawa, Yuji
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)115

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

Modifying the sum over topological sectors and constraints on supergravity
journal, July 2010


Fusion categories and homotopy theory
journal, January 2010

  • Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor
  • Quantum Topology
  • DOI: 10.4171/QT/6

Spectral asymmetry and Riemannian Geometry. I
journal, January 1975

  • Atiyah, M. F.; Patodi, V. K.; Singer, I. M.
  • Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 77, Issue 1
  • DOI: 10.1017/S0305004100049410

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

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

Comments on global symmetries, anomalies, and duality in (2 + 1)d
journal, April 2017

  • Benini, Francesco; Hsin, Po-Shen; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)135

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


Spin TQFTs and fermionic phases of matter
journal, October 2016

  • Gaiotto, Davide; Kapustin, Anton
  • International Journal of Modern Physics A, Vol. 31, Issue 28n29
  • DOI: 10.1142/S0217751X16450445

Interacting fermionic symmetry-protected topological phases in two dimensions
journal, May 2017


Symmetry enforced non-Abelian topological order at the surface of a topological insulator
journal, April 2014


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


The operator algebra of orbifold models
journal, September 1989

  • Dijkgraaf, Robbert; Vafa, Cumrun; Verlinde, Erik
  • Communications in Mathematical Physics, Vol. 123, Issue 3
  • DOI: 10.1007/BF01238812

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
journal, April 2017

  • Bhardwaj, Lakshya; Gaiotto, Davide; Kapustin, Anton
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)096

Condensate-induced transitions between topologically ordered phases
journal, January 2009


Systematic Approach to Cyclic Orbifolds
journal, January 1998

  • Borisov, L.; Halpern, M. B.; Schweigert, C.
  • International Journal of Modern Physics A, Vol. 13, Issue 01
  • DOI: 10.1142/S0217751X98000044

Taming the conformal zoo
journal, April 1989


3d dualities from 4d dualities for orthogonal groups
journal, August 2013

  • Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)099

Seiberg duality in Chern–Simons theory
journal, May 2009


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