Exploring 2-group global symmetries

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

doi:10.1007/JHEP02(2019)184

Title: Exploring 2-group global symmetries

Abstract

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 gaugingmore »« less

Authors:

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)

Publication Date:: Wed Feb 27 00:00:00 EST 2019

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

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

OSTI Identifier:: 1598254

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

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: 2019; Journal Issue: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 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)

Citation Formats


                    Córdova, Clay, Dumitrescu, Thomas T., and Intriligator, Kenneth. Exploring 2-group global symmetries.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP02(2019)184.

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                    Córdova, Clay, Dumitrescu, Thomas T., & Intriligator, Kenneth. Exploring 2-group global symmetries.  United States.  https://doi.org/10.1007/JHEP02(2019)184

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                    Córdova, Clay, Dumitrescu, Thomas T., and Intriligator, Kenneth. Wed .  
"Exploring 2-group global symmetries".  United States.  https://doi.org/10.1007/JHEP02(2019)184.  https://www.osti.gov/servlets/purl/1598254.

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@article{osti_1598254,

  title        = {Exploring 2-group global symmetries},

  author       = {Córdova, Clay and Dumitrescu, Thomas T. and Intriligator, Kenneth},

  abstractNote = {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 JB(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 JB(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 JB(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.},

  doi          = {10.1007/JHEP02(2019)184},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 2,

  volume       = 2019,

  place        = {United States},

  year         = {Wed Feb 27 00:00:00 EST 2019},

  month        = {Wed Feb 27 00:00:00 EST 2019}

}

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Title: Exploring 2-group global symmetries

Abstract

Citation Formats

Gravitational anomalies journal, June 1986

Superstring Theory Volume 1: Introduction Volume 2: Loop Amplitudes, Anomalies and Phenomenology journal, November 1987

New theories in six dimensions and matrix description of M-theory on T5 and journal, September 1997

Limits on massless particles journal, October 1980

Superstrings with torsion journal, September 1986

Supercurrents and brane currents in diverse dimensions journal, July 2011

Anomaly cancellations in supersymmetric D = 10 gauge theory and superstring theory journal, December 1984

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

Gauge theory correlators from non-critical string theory journal, May 1998

Anomaly-free supersymmetric models in six dimensions journal, March 1996

Generalized global symmetries journal, February 2015

Anomalies, renormalization group flows, and the a-theorem in six-dimensional (1, 0) theories journal, October 2016

An SU(2) anomaly journal, November 1982

All free Conformal Representations in all Dimensions journal, May 1989

Anti de Sitter space and holography journal, January 1998

A PCAC puzzle: π0→γγ in the σ-model journal, March 1969

Topological field theory on a lattice, discrete theta-angles and confinement journal, January 2014

Vacuum configurations for superstrings journal, January 1985

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

Zero modes of the vortex-fermion system journal, December 1981

All unitary ray representations of the conformal group SU(2,2) with positive energy text, January 1975

Topological gauge theories and group cohomology journal, April 1990

Consequences of anomalous ward identities journal, November 1971

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

Unified Weak and Electromagnetic Interactions without Neutral Currents journal, May 1972

Small instantons in string theory journal, February 1996

Superconducting strings journal, February 1985

Absence of Higher-Order Corrections in the Anomalous Axial-Vector Divergence Equation journal, June 1969

Symmetry and emergence journal, February 2018

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey journal, March 2018

TASI Lectures on the Emergence of Bulk Physics in AdS/CFT conference, September 2018

Axial-Vector Vertex in Spinor Electrodynamics journal, January 1969

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

Restrictions imposed by superconformal invariance on quantum field theories journal, January 1998

The axial anomaly and the bound-state spectrum in confining theories journal, January 1981

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

All unitary ray representations of the conformal group SU(2,2) with positive energy journal, February 1977

Gravitational anomalies journal, April 1984

String theory journal, July 2009

Notes on generalized global symmetries in QFT: Notes on generalized global symmetries in QFT journal, September 2015

Deformations of superconformal theories journal, November 2016

New = 2 superconformal field theories in four dimensions journal, February 1996

Consistent and covariant anomalies in gauge and gravitational theories journal, October 1984

No more corrections to the topological mass term in QED3 journal, September 1985

Generalized global symmetries and holography journal, January 2018

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

On mirror symmetry in three dimensional Abelian gauge theories journal, April 1999

Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking book, January 1980

't Hooft's consistency condition as a consequence of analyticity and unitarity journal, August 1982

Anomaly polynomial of general 6D SCFTs journal, October 2014

The structure of gauge and gravitational anomalies journal, May 1985

8d gauge anomalies and the topological Green-Schwarz mechanism journal, November 2017

String theory text, January 2020

String theory journal, September 1990

Supercurrents and Brane Currents in Diverse Dimensions text, January 2011

Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories text, January 2012

Comments on Chern-Simons Contact Terms in Three Dimensions text, January 2012

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement preprint, January 2013

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter text, January 2016

Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter text, January 2017

Generalized global symmetries and holography text, January 2017

Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey text, January 2017

Universal Bounds on Operator Dimensions from the Average Null Energy Condition text, January 2017

Small Instantons in String Theory text, January 1995

New N=2 Superconformal Field Theories in Four Dimensions text, January 1995

Anomaly-Free Supersymmetric Models in Six Dimensions text, January 1995

Restrictions Imposed by Superconformal Invariance on Quantum Field Theories text, January 1997

Gauge Theory Correlators from Non-Critical String Theory text, January 1998

Anti De Sitter Space And Holography text, January 1998

Hypercharge quantisation and Fermat's last theorem journal, January 2020

Exceptional Chern-Simons-Matter dualities journal, January 2019

Effective field theory of force-free electrodynamics journal, May 2019

On 2-form gauge models of topological phases journal, May 2019

Dihedral symmetry in S U ( N ) Yang-Mills theory journal, October 2019

Notes on anomalies, elliptic curves and the BS-D conjecture journal, December 2019

On 2-form gauge models of topological phases text, January 2019

Gravitational anomalies
journal, June 1986

Superstring Theory Volume 1: Introduction Volume 2: Loop Amplitudes, Anomalies and Phenomenology
journal, November 1987

New theories in six dimensions and matrix description of M-theory on T5 and
journal, September 1997

Limits on massless particles
journal, October 1980

Superstrings with torsion
journal, September 1986

Supercurrents and brane currents in diverse dimensions
journal, July 2011

Anomaly cancellations in supersymmetric D = 10 gauge theory and superstring theory
journal, December 1984

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

Gauge theory correlators from non-critical string theory
journal, May 1998

Anomaly-free supersymmetric models in six dimensions
journal, March 1996

Generalized global symmetries
journal, February 2015

Anomalies, renormalization group flows, and the a-theorem in six-dimensional (1, 0) theories
journal, October 2016

An SU(2) anomaly
journal, November 1982

All free Conformal Representations in all Dimensions
journal, May 1989

Anti de Sitter space and holography
journal, January 1998

A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969

Topological field theory on a lattice, discrete theta-angles and confinement
journal, January 2014

Vacuum configurations for superstrings
journal, January 1985

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

Zero modes of the vortex-fermion system
journal, December 1981

All unitary ray representations of the conformal group SU(2,2) with positive energy
text, January 1975

Topological gauge theories and group cohomology
journal, April 1990

Consequences of anomalous ward identities
journal, November 1971

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

Unified Weak and Electromagnetic Interactions without Neutral Currents
journal, May 1972

Small instantons in string theory
journal, February 1996

Superconducting strings
journal, February 1985

Absence of Higher-Order Corrections in the Anomalous Axial-Vector Divergence Equation
journal, June 1969

Symmetry and emergence
journal, February 2018

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey
journal, March 2018

TASI Lectures on the Emergence of Bulk Physics in AdS/CFT
conference, September 2018

Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969

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

Restrictions imposed by superconformal invariance on quantum field theories
journal, January 1998

The axial anomaly and the bound-state spectrum in confining theories
journal, January 1981

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

All unitary ray representations of the conformal group SU(2,2) with positive energy
journal, February 1977

Gravitational anomalies
journal, April 1984

String theory
journal, July 2009

Notes on generalized global symmetries in QFT: Notes on generalized global symmetries in QFT
journal, September 2015

Deformations of superconformal theories
journal, November 2016

New = 2 superconformal field theories in four dimensions
journal, February 1996

Consistent and covariant anomalies in gauge and gravitational theories
journal, October 1984

No more corrections to the topological mass term in QED3
journal, September 1985

Generalized global symmetries and holography
journal, January 2018

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

On mirror symmetry in three dimensional Abelian gauge theories
journal, April 1999

Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking
book, January 1980

't Hooft's consistency condition as a consequence of analyticity and unitarity
journal, August 1982

Anomaly polynomial of general 6D SCFTs
journal, October 2014

The structure of gauge and gravitational anomalies
journal, May 1985

8d gauge anomalies and the topological Green-Schwarz mechanism
journal, November 2017

String theory
text, January 2020

String theory
journal, September 1990

Supercurrents and Brane Currents in Diverse Dimensions
text, January 2011

Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
text, January 2012

Comments on Chern-Simons Contact Terms in Three Dimensions
text, January 2012

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement
preprint, January 2013

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
text, January 2016

Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
text, January 2017

Generalized global symmetries and holography
text, January 2017

Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
text, January 2017

Universal Bounds on Operator Dimensions from the Average Null Energy Condition
text, January 2017

Small Instantons in String Theory
text, January 1995

New N=2 Superconformal Field Theories in Four Dimensions
text, January 1995

Anomaly-Free Supersymmetric Models in Six Dimensions
text, January 1995

Restrictions Imposed by Superconformal Invariance on Quantum Field Theories
text, January 1997

Gauge Theory Correlators from Non-Critical String Theory
text, January 1998

Anti De Sitter Space And Holography
text, January 1998

Hypercharge quantisation and Fermat's last theorem
journal, January 2020

Exceptional Chern-Simons-Matter dualities
journal, January 2019

Effective field theory of force-free electrodynamics
journal, May 2019

On 2-form gauge models of topological phases
journal, May 2019

Dihedral symmetry in $S U (N)$ Yang-Mills theory
journal, October 2019

Notes on anomalies, elliptic curves and the BS-D conjecture
journal, December 2019

On 2-form gauge models of topological phases
text, January 2019

On gauging finite subgroups
text, January 2017

On 2-Group Global Symmetries and Their Anomalies
text, January 2018

Effective Field Theory of Force-Free Electrodynamics
text, January 2018