Comments on one-form global symmetries and their gauging in 3d and 4d
Abstract
We study 3d and 4d systems with a one-form global symmetry, explore their consequences, and analyze their gauging. For simplicity, we focus on \mathbb{Z}_N one-form symmetries. A 3d topological quantum field theory (TQFT) \mathcal{T} with such a symmetry has N special lines that generate it. The braiding of these lines and their spins are characterized by a single integer p modulo 2N . Surprisingly, if \gcd(N,p)=1 the TQFT factorizes \mathcal{T}=\mathcal{T}'\otimes \mathcal{A}^{N,p} . Here \mathcal{T}' is a decoupled TQFT, whose lines are neutral under the global symmetry and \mathcal{A}^{N,p} is a minimal TQFT with the \mathbb{Z}_N one-form symmetry of label p . The parameter p labels the obstruction to gauging the \mathbb{Z}_N one-form symmetry; i.e. it characterizes the ’t Hooft anomaly of the global symmetry. When p=0 mod 2N , the symmetry can be gauged. Otherwise, it cannot be gauged unless we couple the system to a 4d bulk with gauge fields extended to the bulk. This understanding allows us to consider SU(N) and PSU(N) 4d gauge theories. Their dynamics is gapped and it is associated with confinement and oblique confinement – probe quarks are confined. In the PSU(N) theory the low-energy theory can include a discrete gauge theory. We will study the behavior of the theory with a space-dependent \theta -parameter, which leads to interfaces. Typically, the theory on the interface is not confining. Furthermore, the liberated probe quarks are anyons on the interface. The PSU(N) theory is obtained by gauging the \mathbb{Z}_N one-form symmetry of the SU(N) theory. Our understanding of the symmetries in 3d TQFTs allows us to describe the interface in the PSU(N) theory.
- Authors:
-
- California Institute of Technology, Princeton University
- Princeton University
- Institute for Advanced Study, Princeton University
- 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:
- 1504279
- Alternate Identifier(s):
- OSTI ID: 1596477
- Grant/Contract Number:
- SC0009988; SC0011632
- Resource Type:
- Published Article
- Journal Name:
- SciPost Physics Proceedings
- Additional Journal Information:
- Journal Name: SciPost Physics Proceedings Journal Volume: 6 Journal Issue: 3; Journal ID: ISSN 2542-4653
- Publisher:
- SciPost Foundation
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Global symmetries; Topological quantum field theories (TQFT)
Citation Formats
Hsin, Po-Shen, Lam, Ho Tat, and Seiberg, Nathan. Comments on one-form global symmetries and their gauging in 3d and 4d. Netherlands: N. p., 2019.
Web. doi:10.21468/SciPostPhys.6.3.039.
Hsin, Po-Shen, Lam, Ho Tat, & Seiberg, Nathan. Comments on one-form global symmetries and their gauging in 3d and 4d. Netherlands. https://doi.org/10.21468/SciPostPhys.6.3.039
Hsin, Po-Shen, Lam, Ho Tat, and Seiberg, Nathan. Fri .
"Comments on one-form global symmetries and their gauging in 3d and 4d". Netherlands. https://doi.org/10.21468/SciPostPhys.6.3.039.
@article{osti_1504279,
title = {Comments on one-form global symmetries and their gauging in 3d and 4d},
author = {Hsin, Po-Shen and Lam, Ho Tat and Seiberg, Nathan},
abstractNote = {We study 3d and 4d systems with a one-form global symmetry, explore their consequences, and analyze their gauging. For simplicity, we focus on \mathbb{Z}_N ℤ N one-form symmetries. A 3d topological quantum field theory (TQFT) \mathcal{T} 𝒯 with such a symmetry has N N special lines that generate it. The braiding of these lines and their spins are characterized by a single integer p p modulo 2N 2 N . Surprisingly, if \gcd(N,p)=1 gcd ( N , p ) = 1 the TQFT factorizes \mathcal{T}=\mathcal{T}'\otimes \mathcal{A}^{N,p} 𝒯 = 𝒯 ′ ⊗ 𝒜 N , p . Here \mathcal{T}' 𝒯 ′ is a decoupled TQFT, whose lines are neutral under the global symmetry and \mathcal{A}^{N,p} 𝒜 N , p is a minimal TQFT with the \mathbb{Z}_N ℤ N one-form symmetry of label p p . The parameter p p labels the obstruction to gauging the \mathbb{Z}_N ℤ N one-form symmetry; i.e. it characterizes the ’t Hooft anomaly of the global symmetry. When p=0 p = 0 mod 2N 2 N , the symmetry can be gauged. Otherwise, it cannot be gauged unless we couple the system to a 4d bulk with gauge fields extended to the bulk. This understanding allows us to consider SU(N) S U ( N ) and PSU(N) P S U ( N ) 4d gauge theories. Their dynamics is gapped and it is associated with confinement and oblique confinement – probe quarks are confined. In the PSU(N) P S U ( N ) theory the low-energy theory can include a discrete gauge theory. We will study the behavior of the theory with a space-dependent \theta θ -parameter, which leads to interfaces. Typically, the theory on the interface is not confining. Furthermore, the liberated probe quarks are anyons on the interface. The PSU(N) P S U ( N ) theory is obtained by gauging the \mathbb{Z}_N ℤ N one-form symmetry of the SU(N) S U ( N ) theory. Our understanding of the symmetries in 3d TQFTs allows us to describe the interface in the PSU(N) P S U ( N ) theory.},
doi = {10.21468/SciPostPhys.6.3.039},
journal = {SciPost Physics Proceedings},
number = 3,
volume = 6,
place = {Netherlands},
year = {Fri Mar 29 00:00:00 EDT 2019},
month = {Fri Mar 29 00:00:00 EDT 2019}
}
https://doi.org/10.21468/SciPostPhys.6.3.039
Web of Science
Works referenced in this record:
Naturality in conformal field theory
journal, January 1989
- Moore, Gregory; Seiberg, Nathan
- Nuclear Physics B, Vol. 313, Issue 1
Catégories prémodulaires, modularisations et invariants des variétés de dimension 3
journal, February 2000
- Bruguières, Alain
- Mathematische Annalen, Vol. 316, Issue 2
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
Anyons in an exactly solved model and beyond
journal, January 2006
- Kitaev, Alexei
- Annals of Physics, Vol. 321, Issue 1
Quadratic forms on finite groups, and related topics
journal, January 1963
- Wall, C. T. C.
- Topology, Vol. 2, Issue 4
Three-dimensional topological lattice models with surface anyons
journal, January 2013
- von Keyserlingk, C. W.; Burnell, F. J.; Simon, S. H.
- Physical Review B, Vol. 87, Issue 4
Theta, time reversal and temperature
journal, May 2017
- Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
- Journal of High Energy Physics, Vol. 2017, Issue 5
On classification of extremal non-holomorphic conformal field theories
journal, February 2017
- Tener, James E.; Wang, Zhenghan
- Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 11
D-brane charges in five-brane backgrounds
journal, October 2001
- Maldacena, Juan; Seiberg, Nathan; Moore, Gregory
- Journal of High Energy Physics, Vol. 2001, Issue 10
Phase transitions in three-dimensional topological lattice models with surface anyons
journal, December 2013
- Burnell, F. J.; von Keyserlingk, C. W.; Simon, S. H.
- Physical Review B, Vol. 88, Issue 23
A study of time reversal symmetry of abelian anyons
journal, July 2018
- Lee, Yasunori; Tachikawa, Yuji
- Journal of High Energy Physics, Vol. 2018, Issue 7
Symmetries and strings in field theory and gravity
journal, April 2011
- Banks, Tom; Seiberg, Nathan
- Physical Review D, Vol. 83, Issue 8
Framed Wilson operators, fermionic strings, and gravitational anomaly in 4d
journal, February 2015
- Thorngren, Ryan
- Journal of High Energy Physics, Vol. 2015, Issue 2
A duality web in dimensions and condensed matter physics
journal, November 2016
- Seiberg, Nathan; Senthil, T.; Wang, Chong
- Annals of Physics, Vol. 374
Level/rank duality and Chern-Simons-matter theories
journal, September 2016
- Hsin, Po-Shen; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2016, Issue 9
Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions
journal, January 2018
- Gaiotto, Davide; Komargodski, Zohar; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2018, Issue 1
Condensate-induced transitions between topologically ordered phases
journal, January 2009
- Bais, F. A.; Slingerland, J. K.
- Physical Review B, Vol. 79, Issue 4
(3+1)-TQFTs and topological insulators
journal, July 2011
- Walker, Kevin; Wang, Zhenghan
- Frontiers of Physics, Vol. 7, Issue 2
Interferometry of non-Abelian anyons
journal, November 2008
- Bonderson, Parsa; Shtengel, Kirill; Slingerland, J. K.
- Annals of Physics, Vol. 323, Issue 11
Topological boundary conditions in abelian Chern–Simons theory
journal, April 2011
- Kapustin, Anton; Saulina, Natalia
- Nuclear Physics B, Vol. 845, Issue 3
Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
journal, January 2018
- Cordova, Clay; Hsin, Po-Shen; Seiberg, Nathan
- SciPost Physics, Vol. 4, Issue 4
Topological field theory on a lattice, discrete theta-angles and confinement
journal, January 2014
- Kapustin, Anton; Thorngren, Ryan
- Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 5
Quadratic Forms on Finite Groups II
journal, July 1972
- Wall, C. T. C.
- Bulletin of the London Mathematical Society, Vol. 4, Issue 2
Taming the conformal zoo
journal, April 1989
- Moore, Gregory; Seiberg, Nathan
- Physics Letters B, Vol. 220, Issue 3
On braided fusion categories I
journal, March 2010
- Drinfeld, Vladimir; Gelaki, Shlomo; Nikshych, Dmitri
- Selecta Mathematica, Vol. 16, Issue 1
Coupling a QFT to a TQFT and duality
journal, April 2014
- Kapustin, Anton; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2014, Issue 4
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
Topological gauge theories and group cohomology
journal, April 1990
- Dijkgraaf, Robbert; Witten, Edward
- Communications in Mathematical Physics, Vol. 129, Issue 2
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
Topological model for domain walls in (super-)Yang-Mills theories
journal, November 2014
- Dierigl, Markus; Pritzel, Alexander
- Physical Review D, Vol. 90, Issue 10