Exploring 2-group global symmetries

Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

doi:10.1007/JHEP02(2019)184

Title: Exploring 2-group global symmetries

Journal Article · Wed Feb 27 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP02(2019)184· OSTI ID:1598254

Córdova, Clay ^[1]; Dumitrescu, Thomas T. ^[2]; Intriligator, Kenneth ^[3]

Inst. for Advanced Study, Princeton, NJ (United States)
Harvard Univ., Cambridge, MA (United States); Univ. of California, Los Angeles, CA (United States)
Univ. of California, San Diego, La Jolla, CA (United States)

Here, we analyze four-dimensional quantum field theories with continuous 2-group global symmetries. At the level of their charges, such symmetries are identical to a product of continuous flavor or spacetime symmetries with a 1-form global symmetry U(1)_B⁽¹⁾, which arises from a conserved 2-form current J_B⁽²⁾. Rather, 2-group symmetries are characterized by deformed current algebras, with quantized structure constants, which allow two flavor currents or stress tensors to fuse into J_B⁽²⁾. This leads to unconventional Ward identities, which constrain the allowed patterns of spontaneous 2-group symmetry breaking and other aspects of the renormalization group flow. If J_B⁽²⁾ is coupled to a 2-form background gauge field B⁽²⁾, the 2-group current algebra modifies the behavior of B⁽²⁾ under background gauge transformations. Its transformation rule takes the same form as in the Green-Schwarz mechanism, but only involves the background gauge or gravity fields that couple to the other 2-group currents. This makes it possible to partially cancel reducible ’t Hooft anomalies using Green-Schwarz counterterms for the 2-group background gauge fields. The parts that cannot be cancelled are reinterpreted as mixed, global anomalies involving U(1)_B⁽¹⁾, which receive contributions from topological, as well as massless, degrees of freedom. Theories with 2-group symmetry are constructed by gauging an abelian flavor symmetry with suitable mixed ’t Hooft anomalies, which leads to many simple and explicit examples. Some of them have dynamical string excitations that carry U(1)_B⁽¹⁾ charge, and 2-group symmetry determines certain ’t Hooft anomalies on the world sheets of these strings. Lastly, we point out that holographic theories with 2-group global symmetries have a bulk description in terms of dynamical gauge fields that participate in a conventional Green-Schwarz mechanism.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF); John Templeton Foundation

Grant/Contract Number:: SC0009988; SC0009919; PHY-1719924; 52476

OSTI ID:: 1598254

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 2; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 125 works

Citation information provided by
Web of Science

References (70)

Gravitational anomalies Leutwyler, H.; Mallik, S. Zeitschrift f�r Physik C Particles and Fields, Vol. 33, Issue 2 https://doi.org/10.1007/bf01411138	journal	June 1986
Superstring Theory Volume 1: Introduction Volume 2: Loop Amplitudes, Anomalies and Phenomenology Green, Michael B.; Schwarz, John H.; Witten, Edward Physics Today, Vol. 40, Issue 11 https://doi.org/10.1063/1.2820272	journal	November 1987
New theories in six dimensions and matrix description of M-theory on T5 and Seiberg, Nathan Physics Letters B, Vol. 408, Issue 1-4 https://doi.org/10.1016/S0370-2693(97)00805-8	journal	September 1997
Limits on massless particles Weinberg, Steven; Witten, Edward Physics Letters B, Vol. 96, Issue 1-2 https://doi.org/10.1016/0370-2693(80)90212-9	journal	October 1980
Superstrings with torsion Strominger, Andrew Nuclear Physics B, Vol. 274, Issue 2 https://doi.org/10.1016/0550-3213(86)90286-5	journal	September 1986
Supercurrents and brane currents in diverse dimensions Dumitrescu, Thomas T.; Seiberg, Nathan Journal of High Energy Physics, Vol. 2011, Issue 7 https://doi.org/10.1007/JHEP07(2011)095	journal	July 2011
Anomaly cancellations in supersymmetric D = 10 gauge theory and superstring theory Green, Michael B.; Schwarz, John H. Physics Letters B, Vol. 149, Issue 1-3 https://doi.org/10.1016/0370-2693(84)91565-X	journal	December 1984
D-brane charges in five-brane backgrounds Maldacena, Juan; Seiberg, Nathan; Moore, Gregory Journal of High Energy Physics, Vol. 2001, Issue 10 https://doi.org/10.1088/1126-6708/2001/10/005	journal	October 2001
Gauge theory correlators from non-critical string theory Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M. Physics Letters B, Vol. 428, Issue 1-2 https://doi.org/10.1016/S0370-2693(98)00377-3	journal	May 1998
Anomaly-free supersymmetric models in six dimensions Schwarz, John H. Physics Letters B, Vol. 371, Issue 3-4 https://doi.org/10.1016/0370-2693(95)01610-4	journal	March 1996
Generalized global symmetries Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan Journal of High Energy Physics, Vol. 2015, Issue 2 https://doi.org/10.1007/JHEP02(2015)172	journal	February 2015
Anomalies, renormalization group flows, and the a-theorem in six-dimensional (1, 0) theories Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)080	journal	October 2016
An SU(2) anomaly Witten, Edward Physics Letters B, Vol. 117, Issue 5 https://doi.org/10.1016/0370-2693(82)90728-6	journal	November 1982
All free Conformal Representations in all Dimensions Siegel, W. International Journal of Modern Physics A, Vol. 04, Issue 08 https://doi.org/10.1142/S0217751X89000819	journal	May 1989
Anti de Sitter space and holography Witten, Edward Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a2	journal	January 1998
A PCAC puzzle: π0→γγ in the σ-model Bell, J. S.; Jackiw, R. Il Nuovo Cimento A, Vol. 60, Issue 1 https://doi.org/10.1007/BF02823296	journal	March 1969
Topological field theory on a lattice, discrete theta-angles and confinement Kapustin, Anton; Thorngren, Ryan Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 5 https://doi.org/10.4310/ATMP.2014.v18.n5.a4	journal	January 2014
Vacuum configurations for superstrings Candelas, P.; Horowitz, Gary T.; Strominger, Andrew Nuclear Physics B, Vol. 258 https://doi.org/10.1016/0550-3213(85)90602-9	journal	January 1985
Coupling a QFT to a TQFT and duality Kapustin, Anton; Seiberg, Nathan Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)001	journal	April 2014
Zero modes of the vortex-fermion system Jackiw, R.; Rossi, P. Nuclear Physics B, Vol. 190, Issue 4 https://doi.org/10.1016/0550-3213(81)90044-4	journal	December 1981
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, Gerhard Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11746	text	January 1975
Topological gauge theories and group cohomology Dijkgraaf, Robbert; Witten, Edward Communications in Mathematical Physics, Vol. 129, Issue 2 https://doi.org/10.1007/BF02096988	journal	April 1990
Consequences of anomalous ward identities Wess, J.; Zumino, B. Physics Letters B, Vol. 37, Issue 1 https://doi.org/10.1016/0370-2693(71)90582-X	journal	November 1971
Modifying the sum over topological sectors and constraints on supergravity Seiberg, Nathan Journal of High Energy Physics, Vol. 2010, Issue 7 https://doi.org/10.1007/JHEP07(2010)070	journal	July 2010
Unified Weak and Electromagnetic Interactions without Neutral Currents Georgi, Howard; Glashow, Sheldon L. Physical Review Letters, Vol. 28, Issue 22 https://doi.org/10.1103/PhysRevLett.28.1494	journal	May 1972
Small instantons in string theory Witten, Edward Nuclear Physics B, Vol. 460, Issue 3 https://doi.org/10.1016/0550-3213(95)00625-7	journal	February 1996
Superconducting strings Witten, Edward Nuclear Physics B, Vol. 249, Issue 4 https://doi.org/10.1016/0550-3213(85)90022-7	journal	February 1985
Absence of Higher-Order Corrections in the Anomalous Axial-Vector Divergence Equation Adler, Stephen L.; Bardeen, William A. Physical Review, Vol. 182, Issue 5 https://doi.org/10.1103/PhysRev.182.1517	journal	June 1969
Symmetry and emergence Witten, Edward Nature Physics, Vol. 14, Issue 2 https://doi.org/10.1038/nphys4348	journal	February 2018
The Large-N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133 https://doi.org/10.1023/A:1026654312961	journal	January 1999
Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/JHEP03(2018)123	journal	March 2018
TASI Lectures on the Emergence of Bulk Physics in AdS/CFT Harlow, Daniel Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017) https://doi.org/10.22323/1.305.0002	conference	September 2018
Axial-Vector Vertex in Spinor Electrodynamics Adler, Stephen L. Physical Review, Vol. 177, Issue 5 https://doi.org/10.1103/PhysRev.177.2426	journal	January 1969
A duality web in $2 + 1$ dimensions and condensed matter physics Seiberg, Nathan; Senthil, T.; Wang, Chong Annals of Physics, Vol. 374 https://doi.org/10.1016/j.aop.2016.08.007	journal	November 2016
Restrictions imposed by superconformal invariance on quantum field theories Minwalla, Shiraz Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 4 https://doi.org/10.4310/ATMP.1998.v2.n4.a4	journal	January 1998
The axial anomaly and the bound-state spectrum in confining theories Frishman, Y.; Schwimmer, A.; Banks, T. Nuclear Physics B, Vol. 177, Issue 1 https://doi.org/10.1016/0550-3213(81)90268-6	journal	January 1981
State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter Bhardwaj, Lakshya; Gaiotto, Davide; Kapustin, Anton Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)096	journal	April 2017
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, G. Communications in Mathematical Physics, Vol. 55, Issue 1 https://doi.org/10.1007/BF01613145	journal	February 1977
Gravitational anomalies Alvarez-Gaumé, Luis; Witten, Edward Nuclear Physics B, Vol. 234, Issue 2 https://doi.org/10.1016/0550-3213(84)90066-X	journal	April 1984
String theory Wilson, J. Engineering & Technology, Vol. 4, Issue 13 https://doi.org/10.1049/et.2009.1314	journal	July 2009
Notes on generalized global symmetries in QFT: Notes on generalized global symmetries in QFT Sharpe, Eric Fortschritte der Physik, Vol. 63, Issue 11-12 https://doi.org/10.1002/prop.201500048	journal	September 2015
Deformations of superconformal theories Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/JHEP11(2016)135	journal	November 2016
New = 2 superconformal field theories in four dimensions Argyres, Philip C.; Ronen Plesser, M.; Seiberg, Nathan Nuclear Physics B, Vol. 461, Issue 1-2 https://doi.org/10.1016/0550-3213(95)00671-0	journal	February 1996
Consistent and covariant anomalies in gauge and gravitational theories Bardeen, William A.; Zumino, Bruno Nuclear Physics B, Vol. 244, Issue 2 https://doi.org/10.1016/0550-3213(84)90322-5	journal	October 1984
No more corrections to the topological mass term in QED3 Coleman, Sidney; Hill, Brian Physics Letters B, Vol. 159, Issue 2-3 https://doi.org/10.1016/0370-2693(85)90883-4	journal	September 1985
Generalized global symmetries and holography Hofman, Diego; Iqbal, Nabil SciPost Physics, Vol. 4, Issue 1 https://doi.org/10.21468/SciPostPhys.4.1.005	journal	January 2018
Time-reversal and spatial-reflection symmetry localization anomalies in (2+1)-dimensional topological phases of matter Barkeshli, Maissam; Cheng, Meng Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115129	journal	September 2018
On mirror symmetry in three dimensional Abelian gauge theories Kapustin, Anton; Strassler, Matthew J. Journal of High Energy Physics, Vol. 1999, Issue 04 https://doi.org/10.1088/1126-6708/1999/04/021	journal	April 1999
Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking Hooft, G. ’t Recent Developments in Gauge Theories https://doi.org/10.1007/978-1-4684-7571-5_9	book	January 1980
't Hooft's consistency condition as a consequence of analyticity and unitarity Coleman, Sidney; Grossman, Bernard Nuclear Physics B, Vol. 203, Issue 2 https://doi.org/10.1016/0550-3213(82)90028-1	journal	August 1982
Anomaly polynomial of general 6D SCFTs Ohmori, K.; Shimizu, H.; Tachikawa, Y. Progress of Theoretical and Experimental Physics, Vol. 2014, Issue 10 https://doi.org/10.1093/ptep/ptu140	journal	October 2014
The structure of gauge and gravitational anomalies Alvarez-Gaumé, Luis; Ginsparg, Paul Annals of Physics, Vol. 161, Issue 2 https://doi.org/10.1016/0003-4916(85)90087-9	journal	May 1985
8d gauge anomalies and the topological Green-Schwarz mechanism García-Etxebarria, Iñaki; Hayashi, Hirotaka; Ohmori, Kantaro Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/JHEP11(2017)177	journal	November 2017
String theory Kabi, Omar Unpublished https://doi.org/10.13140/rg.2.2.30817.94563	text	January 2020
String theory Mansfield, P. Reports on Progress in Physics, Vol. 53, Issue 9 https://doi.org/10.1088/0034-4885/53/9/002	journal	September 1990
Supercurrents and Brane Currents in Diverse Dimensions Dumitrescu, Thomas T.; Seiberg, Nathan arXiv https://doi.org/10.48550/arxiv.1106.0031	text	January 2011
Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories Closset, Cyril; Dumitrescu, Thomas T.; Festuccia, Guido arXiv https://doi.org/10.48550/arxiv.1205.4142	text	January 2012
Comments on Chern-Simons Contact Terms in Three Dimensions Closset, Cyril; Dumitrescu, Thomas T.; Festuccia, Guido arXiv https://doi.org/10.48550/arxiv.1206.5218	text	January 2012
Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement Kapustin, Anton; Thorngren, Ryan arXiv https://doi.org/10.48550/arxiv.1308.2926	preprint	January 2013
State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter Bhardwaj, Lakshya; Gaiotto, Davide; Kapustin, Anton arXiv https://doi.org/10.48550/arxiv.1605.01640	text	January 2016
Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter Barkeshli, Maissam; Cheng, Meng arXiv https://doi.org/10.48550/arxiv.1706.09464	text	January 2017
Generalized global symmetries and holography Hofman, Diego M.; Iqbal, Nabil arXiv https://doi.org/10.48550/arxiv.1707.08577	text	January 2017
Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan arXiv https://doi.org/10.48550/arxiv.1710.08418	text	January 2017
Universal Bounds on Operator Dimensions from the Average Null Energy Condition Cordova, Clay; Diab, Kenan arXiv https://doi.org/10.48550/arxiv.1712.01089	text	January 2017
Small Instantons in String Theory Witten, Edward arXiv https://doi.org/10.48550/arxiv.hep-th/9511030	text	January 1995
New N=2 Superconformal Field Theories in Four Dimensions Argyres, P. C.; Plesser, M. R.; Seiberg, N. arXiv https://doi.org/10.48550/arxiv.hep-th/9511154	text	January 1995
Anomaly-Free Supersymmetric Models in Six Dimensions Schwarz, John H. arXiv https://doi.org/10.48550/arxiv.hep-th/9512053	text	January 1995
Restrictions Imposed by Superconformal Invariance on Quantum Field Theories Minwalla, Shiraz arXiv https://doi.org/10.48550/arxiv.hep-th/9712074	text	January 1997
Gauge Theory Correlators from Non-Critical String Theory Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M. arXiv https://doi.org/10.48550/arxiv.hep-th/9802109	text	January 1998
Anti De Sitter Space And Holography Witten, Edward arXiv https://doi.org/10.48550/arxiv.hep-th/9802150	text	January 1998

Cited By (15)

Hypercharge quantisation and Fermat's last theorem Lohitsiri, Nakarin; Tong, David SciPost Physics, Vol. 8, Issue 1 https://doi.org/10.21468/scipostphys.8.1.009	journal	January 2020
Exceptional Chern-Simons-Matter dualities Cordova, Clay; Hsin, Po-Shen; Ohmori, Kantaro SciPost Physics, Vol. 7, Issue 4 https://doi.org/10.21468/scipostphys.7.4.056	journal	January 2019
Effective field theory of force-free electrodynamics Gralla, Samuel E.; Iqbal, Nabil Physical Review D, Vol. 99, Issue 10 https://doi.org/10.1103/physrevd.99.105004	journal	May 2019
On 2-form gauge models of topological phases Delcamp, Clement; Tiwari, Apoorv Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)064	journal	May 2019
Dihedral symmetry in $S U (N)$ Yang-Mills theory Aitken, Kyle; Cherman, Aleksey; Ünsal, Mithat Physical Review D, Vol. 100, Issue 8 https://doi.org/10.1103/physrevd.100.085004	journal	October 2019
Notes on anomalies, elliptic curves and the BS-D conjecture Lü, Yongchao; Minahan, Joseph A. Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 2 https://doi.org/10.1088/1751-8121/ab5ac3	journal	December 2019
On 2-form gauge models of topological phases Delcamp, Clement; Tiwari, Apoorv Springer https://doi.org/10.5167/uzh-171303	text	January 2019
On gauging finite subgroups Tachikawa, Yuji arXiv https://doi.org/10.48550/arxiv.1712.09542	text	January 2017
On 2-Group Global Symmetries and Their Anomalies Benini, Francesco; Cordova, Clay; Hsin, Po-Shen arXiv https://doi.org/10.48550/arxiv.1803.09336	text	January 2018
Effective Field Theory of Force-Free Electrodynamics Gralla, Samuel E.; Iqbal, Nabil arXiv https://doi.org/10.48550/arxiv.1811.07438	text	January 2018
Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems Wen, Xiao-Gang arXiv https://doi.org/10.48550/arxiv.1812.02517	text	January 2018
Exceptional Chern-Simons-Matter Dualities Cordova, Clay; Hsin, Po-Shen; Ohmori, Kantaro arXiv https://doi.org/10.48550/arxiv.1812.11705	text	January 2018
On 2-form gauge models of topological phases Delcamp, Clement; Tiwari, Apoorv arXiv https://doi.org/10.48550/arxiv.1901.02249	text	January 2019
Anomalies in the Space of Coupling Constants and Their Dynamical Applications I Cordova, Clay; Freed, Daniel S.; Lam, Ho Tat arXiv https://doi.org/10.48550/arxiv.1905.09315	text	January 2019
Anomalies in the Space of Coupling Constants and Their Dynamical Applications II Cordova, Clay; Freed, Daniel S.; Lam, Ho Tat arXiv https://doi.org/10.48550/arxiv.1905.13361	text	January 2019

Similar Records

2-Group global symmetries and anomalies in six-dimensional quantum field theories

Journal Article · Mon Apr 26 00:00:00 EDT 2021 · Journal of High Energy Physics (Online) · OSTI ID:1598254

Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

A theory of R(D*, D) anomaly with right-handed currents

Journal Article · Tue Jan 22 00:00:00 EST 2019 · Journal of High Energy Physics (Online) · OSTI ID:1598254

Babu, K. S.; Dutta, Bhaskar; Mohapatra, Rabindra N.

Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

Journal Article · Wed Jul 03 00:00:00 EDT 2019 · Journal of High Energy Physics (Online) · OSTI ID:1598254

Misumi, Tatsuhiro; Tanizaki, Yuya; Ünsal, Mithat

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
symmetry: global
anomaly: Green-Schwarz
symmetry: flavor
symmetry: space-time
flavor: 2
transformation: gauge
renormalization group: flow
string: excited state
tensor: energy-momentum
dimension: 4
background
gauge field theory
current algebra
field theory
symmetry breaking
conservation law
Ward identity
quantization
gravitation
topological
deformation
holography
abelian
U(1)

Title: Exploring 2-group global symmetries

Citation Formats

References (70)

Cited By (15)

Similar Records

Related Subjects