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

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

doi:10.1007/JHEP07(2020)065

Title: $$\mathcal{N}$$ = (1, 0) anomaly multiplet relations in six dimensions

Abstract

We consider conformal and ’t Hooft anomalies in six-dimensional $$$$ \mathcal{N} $$$$ N = (1, 0) superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and SU(2)R currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non- supersymmetric CFTs in six dimensions have three independent conformal c-anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three c-anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its ’t Hooft anomalies. Following earlier work on the conformal a-anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.

Authors:

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

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

Publication Date:: 2020-07-10

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

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

OSTI Identifier:: 1646659

Alternate Identifier(s):: OSTI ID: 1785448

Grant/Contract Number:: SC0020421; SC0009919

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: 2020; Journal Issue: 7; 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; Conformal Field Theory; Extended Supersymmetry; Field Theories in Higher Dimensions

Citation Formats


                    Córdova, Clay, Dumitrescu, Thomas T., and Intriligator, Kenneth. $\mathcal{N}$ = (1, 0) anomaly multiplet relations in six dimensions.  United States: N. p., 2020. 
Web.  doi:10.1007/JHEP07(2020)065.

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                    Córdova, Clay, Dumitrescu, Thomas T., & Intriligator, Kenneth. $\mathcal{N}$ = (1, 0) anomaly multiplet relations in six dimensions.  United States.  https://doi.org/10.1007/JHEP07(2020)065

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                    Córdova, Clay, Dumitrescu, Thomas T., and Intriligator, Kenneth. Fri .  
"$\mathcal{N}$ = (1, 0) anomaly multiplet relations in six dimensions".  United States.  https://doi.org/10.1007/JHEP07(2020)065.  https://www.osti.gov/servlets/purl/1646659.

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@article{osti_1646659,

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

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

  abstractNote = {We consider conformal and ’t Hooft anomalies in six-dimensional $$ \mathcal{N} $$ N = (1, 0) superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and SU(2)R currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non- supersymmetric CFTs in six dimensions have three independent conformal c-anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three c-anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its ’t Hooft anomalies. Following earlier work on the conformal a-anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.},

  doi          = {10.1007/JHEP07(2020)065},

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

  number       = 7,

  volume       = 2020,

  place        = {United States},

  year         = {2020},

  month        = {7}

}

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Title: $$\mathcal{N}$$ = (1, 0) anomaly multiplet relations in six dimensions

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Branes and six dimensional fixed points journal, September 1997

Causality, analyticity and an IR obstruction to UV completion journal, October 2006

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

Superconformal symmetry and correlation functions journal, October 1999

Supersymmetric R2 actions, conformal invariance and the Lorentz Chern-Simons term in 6 and 10 dimensions journal, January 1987

Anomaly cancellation in seven-dimensional supergravity with a boundary journal, September 2003

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

Anomaly polynomial of E-string theories journal, August 2014

Differential regularization and renormalization: a new method of calculation in quantum field theory journal, March 1992

Superembedding methods for current superfields journal, December 2013

Holographic duals of 6d RG flows journal, March 2019

Anomaly of ( 2 , 0 ) theories journal, October 2001

Toda theory from six dimensions journal, December 2017

Supercurrents and brane currents in diverse dimensions journal, July 2011

AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound journal, March 2010

Universal bounds on operator dimensions from the average null energy condition journal, February 2018

Comments on supercurrent multiplets, supersymmetric field theories and supergravity journal, July 2010

The (2, 0) superconformal bootstrap journal, January 2016

Carving out the end of the world or (superconformal bootstrap in six dimensions) journal, August 2017

Non-local conformal anomalies journal, August 1976

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

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

Small E8 instantons and tensionless non-critical strings journal, August 1996

Holography for (1,0) theories in six dimensions journal, December 2014

Conformal anomaly in Weyl theory and anomaly free superconformal theories journal, January 1984

Spin-2 spectrum of six-dimensional field theories journal, December 2016

A new spin on causality constraints journal, October 2016

Multiplets of superconformal symmetry in diverse dimensions journal, March 2019

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition journal, September 2016

Correlation functions in the CFTd/AdSd+1 correspondence journal, April 1999

Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions journal, January 1997

Counting conformal correlators journal, February 2018

Anomaly polynomial of general 6D SCFTs journal, October 2014

Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in and journal, July 2000

Conformal collider physics: energy and charge correlations journal, May 2008

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

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

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

A holographic computation of the central charges of d = 4, 𝒩 = 2 SCFTs journal, January 2008

Structures on the conformal manifold in six dimensional theories journal, April 2015

Atomic classification of 6D SCFTs: Atomic classification of 6D SCFTs journal, June 2015

Stress-tensor OPE in N = 2 $$ \mathcal{N}=2 $$ superconformal theories journal, February 2016

Bounds on OPE coefficients from interference effects in the conformal collider journal, November 2017

Correlators of the global symmetry currents of 4D and 6D superconformal theories journal, July 1998

5d and 6d SCFTs have no weak coupling limit journal, September 2019

Observations on conformal anomalies journal, July 1977

The trace anomaly of the (2,0) tensor multiplet in background gauge fields journal, May 2000

6d holographic anomaly match as a continuum limit journal, May 2016

Non-abelian tensor-multiplet anomalies journal, September 1998

Superconformal symmetry in six dimensions and its reduction to four journal, February 1999

Averaged null energy condition from causality journal, July 2017

Branes and six-dimensional supersymmetric theories journal, September 1998

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

N=1 Superconformal Symmetry in Four-Dimensional Quantum Field Theory journal, March 1999

W $$ \mathcal{W} $$ symmetry in six dimensions journal, May 2015

Correlation functions of conserved currents in calN = 2 superconformal theory journal, January 2000

Invariants for minimal conformal supergravity in six dimensions journal, December 2016

A proof of the conformal collider bounds journal, June 2016

Implications of Conformal Invariance in Field Theories for General Dimensions journal, May 1994

Supersymmetry in six dimensions journal, July 1983

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

The holographic Weyl anomaly journal, July 1998

Non-perturbative formulas for central functions of supersymmetric gauge theories journal, August 1998

All AdS7 solutions of type II supergravity journal, April 2014

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

Holographic GB gravity in arbitrary dimensions journal, March 2010

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

Deformations of superconformal theories journal, November 2016

On the classification of 6D SCFTs and generalized ADE orbifolds journal, May 2014

Quantum properties of higher dimensional and dimensionally reduced supersymmetric theories journal, October 1983

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

Self-dual 6d 2-form fields coupled to non-abelian gauge field: quantum corrections journal, June 2018

Anomaly matching and a Hopf–Wess–Zumino term in six-dimensional, field theories journal, August 2000

Constraints on parity violating conformal field theories in d = 3
journal, November 2017

Comments on string dynamics in six dimensions
journal, July 1996

Branes and six dimensional fixed points
journal, September 1997

Causality, analyticity and an IR obstruction to UV completion
journal, October 2006

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

Superconformal symmetry and correlation functions
journal, October 1999

Supersymmetric R2 actions, conformal invariance and the Lorentz Chern-Simons term in 6 and 10 dimensions
journal, January 1987

Anomaly cancellation in seven-dimensional supergravity with a boundary
journal, September 2003

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

Anomaly polynomial of E-string theories
journal, August 2014

Differential regularization and renormalization: a new method of calculation in quantum field theory
journal, March 1992

Superembedding methods for current superfields
journal, December 2013

Holographic duals of 6d RG flows
journal, March 2019

Anomaly of $(2, 0)$ theories
journal, October 2001

Toda theory from six dimensions
journal, December 2017

Supercurrents and brane currents in diverse dimensions
journal, July 2011

AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound
journal, March 2010

Universal bounds on operator dimensions from the average null energy condition
journal, February 2018

Comments on supercurrent multiplets, supersymmetric field theories and supergravity
journal, July 2010

The (2, 0) superconformal bootstrap
journal, January 2016

Carving out the end of the world or (superconformal bootstrap in six dimensions)
journal, August 2017

Non-local conformal anomalies
journal, August 1976

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

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

Small E8 instantons and tensionless non-critical strings
journal, August 1996

Holography for (1,0) theories in six dimensions
journal, December 2014

Conformal anomaly in Weyl theory and anomaly free superconformal theories
journal, January 1984

Spin-2 spectrum of six-dimensional field theories
journal, December 2016

A new spin on causality constraints
journal, October 2016

Multiplets of superconformal symmetry in diverse dimensions
journal, March 2019

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Correlation functions in the CFTd/AdSd+1 correspondence
journal, April 1999

Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions
journal, January 1997

Counting conformal correlators
journal, February 2018

Anomaly polynomial of general 6D SCFTs
journal, October 2014

Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in and
journal, July 2000

Conformal collider physics: energy and charge correlations
journal, May 2008

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

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

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

A holographic computation of the central charges of d = 4, 𝒩 = 2 SCFTs
journal, January 2008

Structures on the conformal manifold in six dimensional theories
journal, April 2015

Atomic classification of 6D SCFTs: Atomic classification of 6D SCFTs
journal, June 2015

Stress-tensor OPE in N = 2 $$ \mathcal{N}=2 $$ superconformal theories
journal, February 2016

Bounds on OPE coefficients from interference effects in the conformal collider
journal, November 2017

Correlators of the global symmetry currents of 4D and 6D superconformal theories
journal, July 1998

5d and 6d SCFTs have no weak coupling limit
journal, September 2019

Observations on conformal anomalies
journal, July 1977

The trace anomaly of the (2,0) tensor multiplet in background gauge fields
journal, May 2000

6d holographic anomaly match as a continuum limit
journal, May 2016

Non-abelian tensor-multiplet anomalies
journal, September 1998

Superconformal symmetry in six dimensions and its reduction to four
journal, February 1999

Averaged null energy condition from causality
journal, July 2017

Branes and six-dimensional supersymmetric theories
journal, September 1998

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

N=1 Superconformal Symmetry in Four-Dimensional Quantum Field Theory
journal, March 1999

W $$ \mathcal{W} $$ symmetry in six dimensions
journal, May 2015

Correlation functions of conserved currents in calN = 2 superconformal theory
journal, January 2000

Invariants for minimal conformal supergravity in six dimensions
journal, December 2016

A proof of the conformal collider bounds
journal, June 2016

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

Supersymmetry in six dimensions
journal, July 1983

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

The holographic Weyl anomaly
journal, July 1998

Non-perturbative formulas for central functions of supersymmetric gauge theories
journal, August 1998

All AdS7 solutions of type II supergravity
journal, April 2014

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

Holographic GB gravity in arbitrary dimensions
journal, March 2010

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

Deformations of superconformal theories
journal, November 2016

On the classification of 6D SCFTs and generalized ADE orbifolds
journal, May 2014

Quantum properties of higher dimensional and dimensionally reduced supersymmetric theories
journal, October 1983

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

Self-dual 6d 2-form fields coupled to non-abelian gauge field: quantum corrections
journal, June 2018

Anomaly matching and a Hopf–Wess–Zumino term in six-dimensional, field theories
journal, August 2000

R-currents and trace anomalies in the (2,0) tensor multiplet in d=6 and AdS/CFT correspondence
journal, June 2000

Geometry of 6D RG flows
journal, September 2015

Current OPEs in superconformal theories
journal, September 2011