Anomalies in the space of coupling constants and their dynamical applications I

doi:10.21468/SciPostPhys.8.1.001

Title: Anomalies in the space of coupling constants and their dynamical applications I

Abstract

It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields (and a metric for the Poincaré symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects ’t Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of ’t Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary ’t Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized ’t Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to thismore »« less

Authors:

Cordova, Clay ^[1]; Freed, Daniel ^[2]; Lam, Ho Tat ^[3]; Seiberg, Nathan ^[1]

Institute for Advanced Study, Princeton University
The University of Texas at Austin
Princeton University

Publication Date:: 2020-01-06

Sponsoring Org.:: USDOE

OSTI Identifier:: 1581204

Grant/Contract Number:: SC0009988

Resource Type:: Published Article

Journal Name:: SciPost Physics Proceedings

Additional Journal Information:: Journal Name: SciPost Physics Proceedings Journal Volume: 8 Journal Issue: 1; Journal ID: ISSN 2542-4653

Publisher:: Stichting SciPost

Country of Publication:: Netherlands

Language:: English

Citation Formats


                    Cordova, Clay, Freed, Daniel, Lam, Ho Tat, and Seiberg, Nathan. Anomalies in the space of coupling constants and their dynamical applications I.  Netherlands: N. p., 2020. 
        Web.  doi:10.21468/SciPostPhys.8.1.001.

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                    Cordova, Clay, Freed, Daniel, Lam, Ho Tat, & Seiberg, Nathan. Anomalies in the space of coupling constants and their dynamical applications I.  Netherlands.  doi:10.21468/SciPostPhys.8.1.001.

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                    Cordova, Clay, Freed, Daniel, Lam, Ho Tat, and Seiberg, Nathan. Mon .  
        "Anomalies in the space of coupling constants and their dynamical applications I".  Netherlands.  doi:10.21468/SciPostPhys.8.1.001.

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@article{osti_1581204,

  title        = {Anomalies in the space of coupling constants and their dynamical applications I},

  author       = {Cordova, Clay and Freed, Daniel and Lam, Ho Tat and Seiberg, Nathan},

  abstractNote = {It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields (and a metric for the Poincaré symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects ’t Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of ’t Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary ’t Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized ’t Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to this perspective. Also, we use Quillen’s superconnections to derive the anomaly for a free spinor field with variable mass. In a companion paper we will study four-dimensional gauge theories showing how our view unifies and extends many recently obtained results.},

  doi          = {10.21468/SciPostPhys.8.1.001},

  journal      = {SciPost Physics Proceedings},

  number       = 1,

  volume       = 8,

  place        = {Netherlands},

  year         = {2020},

  month        = {1}

}

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Title: Anomalies in the space of coupling constants and their dynamical applications I

Abstract

Citation Formats

Anomalies, conformal manifolds, and spheres journal, March 2016

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

Differential cohomology theories as sheaves of spectra journal, October 2014

Spectral asymmetry and Riemannian geometry. II journal, November 1975

Theta, time reversal and temperature journal, May 2017

Comments on one-form global symmetries and their gauging in 3d and 4d journal, January 2019

Non-Birational Twisted Derived Equivalences in Abelian GLSMs journal, December 2009

Anomalies and fermion zero modes on strings and domain walls journal, January 1985

Osborn equation and irrelevant operators journal, August 2019

Conformal field theories and compact curves in moduli spaces journal, May 2018

Generalization of the Haldane conjecture to SU(3) chains journal, November 2017

Heisenberg groups and noncommutative fluxes journal, January 2007

A note on the (∞,n)–category of cobordisms journal, January 2019

Anomalies and odd dimensions journal, September 1985

Generalized global symmetries journal, February 2015

Theories of class F and anomalies journal, October 2018

Nonlinear σ model at θ=π: Euclidean lattice formulation and solid-on-solid models journal, May 1991

Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions journal, January 2018

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj) journal, May 2019

Critical theory of quantum spin chains journal, October 1987

Setting the Quantum Integrand of M-Theory journal, January 2006

G{LSM}s for gerbes (and other toric stacks) journal, January 2006

Time-reversal symmetry, anomalies, and dualities in (2+1)$d$ journal, January 2018

Topological mass term for gravity induced by matter journal, October 1986

Relative Quantum Field Theory journal, January 2014

Phases Of Adjoint QCD$_3$ And Dualities journal, January 2018

Anomalies of duality groups and extended conformal manifolds journal, July 2018

Superconnections and index theory journal, August 2011

Exceptional Chern-Simons-Matter dualities journal, January 2019

Algebraic and Hamiltonian methods in the theory of non-Abelian anomalies journal, August 1984

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

The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade journal, May 2019

Gapped boundary phases of topological insulators via weak coupling journal, November 2016

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

Topological quantization and cohomology journal, June 1985

Superconnections and the Chern character journal, January 1985

Spectral asymmetry and Riemannian Geometry. I journal, January 1975

A symmetry breaking scenario for QCD3 journal, January 2018

Comments on abelian Higgs models and persistent order journal, January 2019

More about the massive Schwinger model journal, September 1976

Superconducting strings journal, February 1985

Origins of global anomalies in quantum mechanics journal, August 1986

Comments on global symmetries, anomalies, and duality in (2 + 1)d journal, April 2017

Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics journal, November 2017

Moduli anomalies and local terms in the operator product expansion journal, July 2018

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

Level/rank duality and Chern-Simons-matter theories journal, September 2016

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1 journal, February 2019

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups journal, January 2018

Walls, anomalies, and deconfinement in quantum antiferromagnets journal, February 2018

Chern–Weil forms and abstract homotopy theory journal, April 2013

Living on the walls of super-QCD journal, January 2019

Axial anomalies and index theorems on open spaces journal, October 1978

Sigma models on flags journal, January 2019

Some remarks on the paper of Callias journal, October 1978

Three-dimensional dualities with bosons and fermions journal, February 2018

Anomalies involving the space of couplings and the Zamolodchikov metric journal, December 2017

Shortening anomalies in supersymmetric theories journal, January 2017

Anomaly and global inconsistency matching: θ angles, S U ( 3 ) / U ( 1 ) 2 nonlinear sigma model, S U ( 3 ) chains, and generalizations journal, September 2018

Chern-Simons-matter dualities with SO and USp gauge groups journal, February 2017

Exploring 2-group global symmetries journal, February 2019

Anomalies, conformal manifolds, and spheres
journal, March 2016

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

Differential cohomology theories as sheaves of spectra
journal, October 2014

Spectral asymmetry and Riemannian geometry. II
journal, November 1975

Theta, time reversal and temperature
journal, May 2017

Comments on one-form global symmetries and their gauging in 3d and 4d
journal, January 2019

Non-Birational Twisted Derived Equivalences in Abelian GLSMs
journal, December 2009

Anomalies and fermion zero modes on strings and domain walls
journal, January 1985

Osborn equation and irrelevant operators
journal, August 2019

Conformal field theories and compact curves in moduli spaces
journal, May 2018

Generalization of the Haldane conjecture to SU(3) chains
journal, November 2017

Heisenberg groups and noncommutative fluxes
journal, January 2007

A note on the (∞,n)–category of cobordisms
journal, January 2019

Anomalies and odd dimensions
journal, September 1985

Generalized global symmetries
journal, February 2015

Theories of class F and anomalies
journal, October 2018

Nonlinear σ model at θ=π: Euclidean lattice formulation and solid-on-solid models
journal, May 1991

Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions
journal, January 2018

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
journal, May 2019

Critical theory of quantum spin chains
journal, October 1987

Setting the Quantum Integrand of M-Theory
journal, January 2006

G{LSM}s for gerbes (and other toric stacks)
journal, January 2006

Time-reversal symmetry, anomalies, and dualities in (2+1)$d$
journal, January 2018

Topological mass term for gravity induced by matter
journal, October 1986

Relative Quantum Field Theory
journal, January 2014

Phases Of Adjoint QCD$_3$ And Dualities
journal, January 2018

Anomalies of duality groups and extended conformal manifolds
journal, July 2018

Superconnections and index theory
journal, August 2011

Exceptional Chern-Simons-Matter dualities
journal, January 2019

Algebraic and Hamiltonian methods in the theory of non-Abelian anomalies
journal, August 1984

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

The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade
journal, May 2019

Gapped boundary phases of topological insulators via weak coupling
journal, November 2016

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

Topological quantization and cohomology
journal, June 1985

Superconnections and the Chern character
journal, January 1985

Spectral asymmetry and Riemannian Geometry. I
journal, January 1975

A symmetry breaking scenario for QCD3
journal, January 2018

Comments on abelian Higgs models and persistent order
journal, January 2019

More about the massive Schwinger model
journal, September 1976

Superconducting strings
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Origins of global anomalies in quantum mechanics
journal, August 1986

Comments on global symmetries, anomalies, and duality in (2 + 1)d
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Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics
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Moduli anomalies and local terms in the operator product expansion
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A duality web in $2 + 1$ dimensions and condensed matter physics
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Level/rank duality and Chern-Simons-matter theories
journal, September 2016

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1
journal, February 2019

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
journal, January 2018

Walls, anomalies, and deconfinement in quantum antiferromagnets
journal, February 2018

Chern–Weil forms and abstract homotopy theory
journal, April 2013

Living on the walls of super-QCD
journal, January 2019

Axial anomalies and index theorems on open spaces
journal, October 1978

Sigma models on flags
journal, January 2019

Some remarks on the paper of Callias
journal, October 1978

Three-dimensional dualities with bosons and fermions
journal, February 2018

Anomalies involving the space of couplings and the Zamolodchikov metric
journal, December 2017

Shortening anomalies in supersymmetric theories
journal, January 2017

Anomaly and global inconsistency matching: $θ$ angles, $S U (3) / U {(1)}^{2}$ nonlinear sigma model, $S U (3)$ chains, and generalizations
journal, September 2018

Chern-Simons-matter dualities with SO and USp gauge groups
journal, February 2017

Exploring 2-group global symmetries
journal, February 2019