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

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

doi:10.1007/jhep04(2021)252

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

Abstract

We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength ƒ⁽²⁾, naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J⁽²⁾~ _*Tr (ƒ⁽²⁾ $$\wedge$$ ƒ⁽²⁾). We show that suitable mixed anomalies involving the gauge field ƒ⁽²⁾ and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J⁽²⁾. We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.

Authors:

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

Univ. of Chicago, IL (United States). Enrico Fermi Inst.
Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Theoretical Physics
Univ. of California, San Diego, CA (United States)

Publication Date:: Mon Apr 26 00:00:00 EDT 2021

Research Org.:: Univ. of California, Los Angeles, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1785447

Grant/Contract Number:: SC0020421; SC0021432; SC0009919; 568420

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: 2021; Journal Issue: 4; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Field Theories in Higher Dimensions; Renormalization Group; Supersymmetric Gauge Theory

Citation Formats


                    Córdova, Clay, Dumitrescu, Thomas T., and Intriligator, Kenneth. 2-Group global symmetries and anomalies in six-dimensional quantum field theories.  United States: N. p., 2021. 
Web.  doi:10.1007/jhep04(2021)252.

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                    Córdova, Clay, Dumitrescu, Thomas T., & Intriligator, Kenneth. 2-Group global symmetries and anomalies in six-dimensional quantum field theories.  United States.  https://doi.org/10.1007/jhep04(2021)252

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                    Córdova, Clay, Dumitrescu, Thomas T., and Intriligator, Kenneth. Mon .  
"2-Group global symmetries and anomalies in six-dimensional quantum field theories".  United States.  https://doi.org/10.1007/jhep04(2021)252.  https://www.osti.gov/servlets/purl/1785447.

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@article{osti_1785447,

  title        = {2-Group global symmetries and anomalies in six-dimensional quantum field theories},

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

  abstractNote = {We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength ƒ(2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J(2)~ *Tr (ƒ(2) $\wedge$ ƒ(2)). We show that suitable mixed anomalies involving the gauge field ƒ(2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J(2). We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.},

  doi          = {10.1007/jhep04(2021)252},

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

  number       = 4,

  volume       = 2021,

  place        = {United States},

  year         = {Mon Apr 26 00:00:00 EDT 2021},

  month        = {Mon Apr 26 00:00:00 EDT 2021}

}

Copy to clipboard

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

Abstract

Citation Formats

Is there a c-theorem in four dimensions? journal, December 1988

AdS7/CFT6 with orientifolds journal, January 2018

A comment on sigma model anomalies journal, February 1985

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

Branes and six dimensional fixed points journal, September 1997

Geometric classification of conformal anomalies in arbitrary dimensions journal, July 1993

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

Evidence for C-theorems in 6D SCFTs journal, September 2015

A brief review of `little string theories' journal, February 2000

Supercurrents and brane currents in diverse dimensions journal, July 2011

New string theories in six dimensions via branes at orbifold singularities journal, January 1997

Comments on the IIA NS5-brane journal, June 1999

Anomaly of strings of 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ theories journal, November 2016

$$ \mathcal{N} $$ = (1, 0) anomaly multiplet relations in six dimensions journal, July 2020

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

Higher derivative terms, toroidal compactification, and Weyl anomalies in six-dimensional (2, 0) theories journal, October 2019

Multiplets of superconformal symmetry in diverse dimensions journal, March 2019

Universality class of little string theories journal, March 2001

Anomaly-free chiral theories in six dimensions journal, January 1985

What Maxwell theory in teaches us about scale and conformal invariance journal, July 2011

Anomaly polynomial of general 6D SCFTs journal, October 2014

Universal features of BPS strings in six-dimensional SCFTs journal, August 2018

On renormalization group flows and the a-theorem in 6d journal, October 2012

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

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

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

Conformal properties of hypermultiplet actions in six dimensions journal, June 2006

Chiral anomalies in higher-derivative supersymmetric 6D gauge theories journal, April 2007

C T for higher derivative conformal fields and anomalies of (1, 0) superconformal 6d theories journal, June 2017

On gauging finite subgroups journal, January 2020

The structure of gauge and gravitational anomalies journal, May 1985

Higher-form symmetries in 5d journal, September 2020

Discrete theta angles, symmetries and anomalies journal, January 2021

Small instantons in string theory journal, February 1996

Renormalization group flows, the a-theorem and conformal bootstrap journal, May 2020

Tutorial on scale and conformal symmetries in diverse dimensions journal, May 2011

UV-IR relations in AdS dynamics journal, February 1999

A note on the Green-Schwarz mechanism in open-string theories journal, November 1992

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

Branes and six-dimensional supersymmetric theories journal, September 1998

Mirror symmetry in three dimensional gauge theories journal, October 1996

Top down approach to 6D SCFTs journal, February 2019

Supersymmetric AdS7 backgrounds in half-maximal supergravity and marginal operators of (1, 0) SCFTs journal, October 2015

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

Non-trivial fixed points of the renormalization group in six dimensions journal, January 1997

On renormalization group flows in four dimensions journal, December 2011

Gravitational anomalies journal, April 1984

Supersymmetric Rényi entropy and Anomalies in 6d (1,0) SCFTs journal, April 2017

Branes at orbifolds versus Hanany Witten in six dimensions journal, March 1998

Deformations of superconformal theories journal, November 2016

Conformal a-anomaly of some non-unitary 6d superconformal theories journal, September 2015

New phases of string theory and 6d RG fixed points via branes at orbifold singularities journal, November 1997

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories journal, February 2019

Higher-form symmetries of 6d and 5d theories journal, February 2021

Semiclassical decay of near extremal fivebranes journal, December 1997

Exploring 2-group global symmetries journal, February 2019

6d, N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ Coulomb branch anomaly matching journal, October 2014

The structure of gauge and gravitational anomalies journal, May 1985

Chiral anomalies in higher-derivative supersymmetric 6D gauge theories journal, April 2007

Comments on the IIA NS5-brane journal, June 1999

L-infinity algebra connections and applications to String- and Chern-Simons n-transport text, January 2008

Connections on non-abelian Gerbes and their Holonomy text, January 2008

Coupling a QFT to a TQFT and Duality text, January 2014

Top Down Approach to 6D SCFTs text, January 2018

Is there a c-theorem in four dimensions?
journal, December 1988

AdS7/CFT6 with orientifolds
journal, January 2018

A comment on sigma model anomalies
journal, February 1985

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

Branes and six dimensional fixed points
journal, September 1997

Geometric classification of conformal anomalies in arbitrary dimensions
journal, July 1993

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

Evidence for C-theorems in 6D SCFTs
journal, September 2015

A brief review of `little string theories'
journal, February 2000

Supercurrents and brane currents in diverse dimensions
journal, July 2011

New string theories in six dimensions via branes at orbifold singularities
journal, January 1997

Comments on the IIA NS5-brane
journal, June 1999

Anomaly of strings of 6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ theories
journal, November 2016

$$ \mathcal{N} $$ = (1, 0) anomaly multiplet relations in six dimensions
journal, July 2020

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

Higher derivative terms, toroidal compactification, and Weyl anomalies in six-dimensional (2, 0) theories
journal, October 2019

Multiplets of superconformal symmetry in diverse dimensions
journal, March 2019

Universality class of little string theories
journal, March 2001

Anomaly-free chiral theories in six dimensions
journal, January 1985

What Maxwell theory in teaches us about scale and conformal invariance
journal, July 2011

Anomaly polynomial of general 6D SCFTs
journal, October 2014

Universal features of BPS strings in six-dimensional SCFTs
journal, August 2018

On renormalization group flows and the a-theorem in 6d
journal, October 2012

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

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

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

Conformal properties of hypermultiplet actions in six dimensions
journal, June 2006

Chiral anomalies in higher-derivative supersymmetric 6D gauge theories
journal, April 2007

C T for higher derivative conformal fields and anomalies of (1, 0) superconformal 6d theories
journal, June 2017

On gauging finite subgroups
journal, January 2020

The structure of gauge and gravitational anomalies
journal, May 1985

Higher-form symmetries in 5d
journal, September 2020

Discrete theta angles, symmetries and anomalies
journal, January 2021

Small instantons in string theory
journal, February 1996

Renormalization group flows, the a-theorem and conformal bootstrap
journal, May 2020

Tutorial on scale and conformal symmetries in diverse dimensions
journal, May 2011

UV-IR relations in AdS dynamics
journal, February 1999

A note on the Green-Schwarz mechanism in open-string theories
journal, November 1992

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

Branes and six-dimensional supersymmetric theories
journal, September 1998

Mirror symmetry in three dimensional gauge theories
journal, October 1996

Top down approach to 6D SCFTs
journal, February 2019

Supersymmetric AdS7 backgrounds in half-maximal supergravity and marginal operators of (1, 0) SCFTs
journal, October 2015

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

Non-trivial fixed points of the renormalization group in six dimensions
journal, January 1997

On renormalization group flows in four dimensions
journal, December 2011

Gravitational anomalies
journal, April 1984

Supersymmetric Rényi entropy and Anomalies in 6d (1,0) SCFTs
journal, April 2017

Branes at orbifolds versus Hanany Witten in six dimensions
journal, March 1998

Deformations of superconformal theories
journal, November 2016

Conformal a-anomaly of some non-unitary 6d superconformal theories
journal, September 2015

New phases of string theory and 6d RG fixed points via branes at orbifold singularities
journal, November 1997

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories
journal, February 2019

Higher-form symmetries of 6d and 5d theories
journal, February 2021

Semiclassical decay of near extremal fivebranes
journal, December 1997

Exploring 2-group global symmetries
journal, February 2019

6d, N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ Coulomb branch anomaly matching
journal, October 2014

The structure of gauge and gravitational anomalies
journal, May 1985

Chiral anomalies in higher-derivative supersymmetric 6D gauge theories
journal, April 2007

Comments on the IIA NS5-brane
journal, June 1999

L-infinity algebra connections and applications to String- and Chern-Simons n-transport
text, January 2008

Connections on non-abelian Gerbes and their Holonomy
text, January 2008

Coupling a QFT to a TQFT and Duality
text, January 2014

Top Down Approach to 6D SCFTs
text, January 2018