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 »
- Authors:
-
- Institute for Advanced Study, Princeton University
- The University of Texas at Austin
- Princeton University
- Publication Date:
- Research Org.:
- Institute for Advanced Study, Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1581204
- Alternate Identifier(s):
- OSTI ID: 1801989
- 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
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics
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.
Cordova, Clay, Freed, Daniel, Lam, Ho Tat, & Seiberg, Nathan. Anomalies in the space of coupling constants and their dynamical applications I. Netherlands. https://doi.org/10.21468/SciPostPhys.8.1.001
Cordova, Clay, Freed, Daniel, Lam, Ho Tat, and Seiberg, Nathan. Mon .
"Anomalies in the space of coupling constants and their dynamical applications I". Netherlands. https://doi.org/10.21468/SciPostPhys.8.1.001.
@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}
}
https://doi.org/10.21468/SciPostPhys.8.1.001
Web of Science
Works referenced in this record:
Anomalies, conformal manifolds, and spheres
journal, March 2016
- Gomis, Jaume; Hsin, Po-Shen; Komargodski, Zohar
- Journal of High Energy Physics, Vol. 2016, Issue 3
On 2-group global symmetries and their anomalies
journal, March 2019
- Benini, Francesco; Córdova, Clay; Hsin, Po-Shen
- Journal of High Energy Physics, Vol. 2019, Issue 3
Differential cohomology theories as sheaves of spectra
journal, October 2014
- Bunke, Ulrich; Nikolaus, Thomas; Völkl, Michael
- Journal of Homotopy and Related Structures, Vol. 11, Issue 1
Spectral asymmetry and Riemannian geometry. II
journal, November 1975
- Atiyah, M. F.; Patodi, V. K.; Singer, I. M.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 78, Issue 3
Theta, time reversal and temperature
journal, May 2017
- Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
- Journal of High Energy Physics, Vol. 2017, Issue 5
Comments on one-form global symmetries and their gauging in 3d and 4d
journal, January 2019
- Hsin, Po-Shen; Lam, Ho Tat; Seiberg, Nathan
- SciPost Physics, Vol. 6, Issue 3
Non-Birational Twisted Derived Equivalences in Abelian GLSMs
journal, December 2009
- Căldăraru, Andrei; Distler, Jacques; Hellerman, Simeon
- Communications in Mathematical Physics, Vol. 294, Issue 3
Anomalies and fermion zero modes on strings and domain walls
journal, January 1985
- Callan, C. G.; Harvey, J. A.
- Nuclear Physics B, Vol. 250, Issue 1-4
Osborn equation and irrelevant operators
journal, August 2019
- Schwimmer, Adam; Theisen, Stefan
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 8
Conformal field theories and compact curves in moduli spaces
journal, May 2018
- Donagi, Ron; Morrison, David R.
- Journal of High Energy Physics, Vol. 2018, Issue 5
Generalization of the Haldane conjecture to SU(3) chains
journal, November 2017
- Lajkó, Miklós; Wamer, Kyle; Mila, Frédéric
- Nuclear Physics B, Vol. 924
Heisenberg groups and noncommutative fluxes
journal, January 2007
- Freed, Daniel S.; Moore, Gregory W.; Segal, Graeme
- Annals of Physics, Vol. 322, Issue 1
A note on the (∞,n)–category of cobordisms
journal, January 2019
- Calaque, Damien; Scheimbauer, Claudia
- Algebraic & Geometric Topology, Vol. 19, Issue 2
Anomalies and odd dimensions
journal, September 1985
- Alvarez-Gaumé, L.; Della Pietra, S.; Moore, G.
- Annals of Physics, Vol. 163, Issue 2
Generalized global symmetries
journal, February 2015
- Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2015, Issue 2
Theories of class F and anomalies
journal, October 2018
- Lawrie, Craig; Martelli, Dario; Schäfer-Nameki, Sakura
- Journal of High Energy Physics, Vol. 2018, Issue 10
Nonlinear σ model at θ=π: Euclidean lattice formulation and solid-on-solid models
journal, May 1991
- Affleck, Ian
- Physical Review Letters, Vol. 66, Issue 19
Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions
journal, January 2018
- Gaiotto, Davide; Komargodski, Zohar; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2018, Issue 1
Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
journal, May 2019
- Anber, Mohamed M.; Poppitz, Erich
- Journal of High Energy Physics, Vol. 2019, Issue 5
Critical theory of quantum spin chains
journal, October 1987
- Affleck, Ian; Haldane, F. D. M.
- Physical Review B, Vol. 36, Issue 10
Setting the Quantum Integrand of M-Theory
journal, January 2006
- Freed, Daniel S.; Moore, Gregory W.
- Communications in Mathematical Physics, Vol. 263, Issue 1
G{LSM}s for gerbes (and other toric stacks)
journal, January 2006
- Pantev, Tony; Sharpe, Eric
- Advances in Theoretical and Mathematical Physics, Vol. 10, Issue 1
Time-reversal symmetry, anomalies, and dualities in (2+1)$d$
journal, January 2018
- Cordova, Clay; Hsin, Po-Shen; Seiberg, Nathan
- SciPost Physics, Vol. 5, Issue 1
Topological mass term for gravity induced by matter
journal, October 1986
- Van Der Bij, J. J.; Pisarski, Robert D.; Rao, Sumathi
- Physics Letters B, Vol. 179, Issue 1-2
Relative Quantum Field Theory
journal, January 2014
- Freed, Daniel S.; Teleman, Constantin
- Communications in Mathematical Physics, Vol. 326, Issue 2
Phases Of Adjoint QCD$_3$ And Dualities
journal, January 2018
- Gomis, Jaume; Komargodski, Zohar; Seiberg, Nathan
- SciPost Physics, Vol. 5, Issue 1
Anomalies of duality groups and extended conformal manifolds
journal, July 2018
- Seiberg, Nathan; Tachikawa, Yuji; Yonekura, Kazuya
- Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 7
Superconnections and index theory
journal, August 2011
- Kahle, Alexander
- Journal of Geometry and Physics, Vol. 61, Issue 8
Exceptional Chern-Simons-Matter dualities
journal, January 2019
- Cordova, Clay; Hsin, Po-Shen; Ohmori, Kantaro
- SciPost Physics, Vol. 7, Issue 4
Algebraic and Hamiltonian methods in the theory of non-Abelian anomalies
journal, August 1984
- Faddeev, L. D.; Shatashvili, S. L.
- Theoretical and Mathematical Physics, Vol. 60, Issue 2
Zero modes of the vortex-fermion system
journal, December 1981
- Jackiw, R.; Rossi, P.
- Nuclear Physics B, Vol. 190, Issue 4
The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade
journal, May 2019
- Karasik, Avner; Komargodski, Zohar
- Journal of High Energy Physics, Vol. 2019, Issue 5
Gapped boundary phases of topological insulators via weak coupling
journal, November 2016
- Seiberg, Nathan; Witten, Edward
- Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12
Modifying the sum over topological sectors and constraints on supergravity
journal, July 2010
- Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2010, Issue 7
Topological quantization and cohomology
journal, June 1985
- Alvarez, Orlando
- Communications in Mathematical Physics, Vol. 100, Issue 2
Superconnections and the Chern character
journal, January 1985
- Quillen, Daniel
- Topology, Vol. 24, Issue 1
Spectral asymmetry and Riemannian Geometry. I
journal, January 1975
- Atiyah, M. F.; Patodi, V. K.; Singer, I. M.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 77, Issue 1
A symmetry breaking scenario for QCD3
journal, January 2018
- Komargodski, Zohar; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2018, Issue 1
Comments on abelian Higgs models and persistent order
journal, January 2019
- Komargodski, Zohar; Sharon, Adar; Thorngren, Ryan
- SciPost Physics, Vol. 6, Issue 1
More about the massive Schwinger model
journal, September 1976
- Coleman, Sidney
- Annals of Physics, Vol. 101, Issue 1
Origins of global anomalies in quantum mechanics
journal, August 1986
- Elitzur, S.; Rabinovici, E.; Frishman, Y.
- Nuclear Physics B, Vol. 273, Issue 1
Comments on global symmetries, anomalies, and duality in (2 + 1)d
journal, April 2017
- Benini, Francesco; Hsin, Po-Shen; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2017, Issue 4
Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics
journal, November 2017
- Kikuchi, Yuta; Tanizaki, Yuya
- Progress of Theoretical and Experimental Physics, Vol. 2017, Issue 11
Moduli anomalies and local terms in the operator product expansion
journal, July 2018
- Schwimmer, Adam; Theisen, Stefan
- Journal of High Energy Physics, Vol. 2018, Issue 7
A duality web in dimensions and condensed matter physics
journal, November 2016
- Seiberg, Nathan; Senthil, T.; Wang, Chong
- Annals of Physics, Vol. 374
Level/rank duality and Chern-Simons-matter theories
journal, September 2016
- Hsin, Po-Shen; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2016, Issue 9
Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S1
journal, February 2019
- Hongo, Masaru; Misumi, Tatsuhiro; Tanizaki, Yuya
- Journal of High Energy Physics, Vol. 2019, Issue 2
Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
journal, January 2018
- Cordova, Clay; Hsin, Po-Shen; Seiberg, Nathan
- SciPost Physics, Vol. 4, Issue 4
Walls, anomalies, and deconfinement in quantum antiferromagnets
journal, February 2018
- Komargodski, Zohar; Sulejmanpasic, Tin; Ünsal, Mithat
- Physical Review B, Vol. 97, Issue 5
Chern–Weil forms and abstract homotopy theory
journal, April 2013
- Freed, Daniel S.; Hopkins, Michael J.
- Bulletin of the American Mathematical Society, Vol. 50, Issue 3
Living on the walls of super-QCD
journal, January 2019
- Bashmakov, Vladimir; Benini, Francesco; Benvenuti, Sergio
- SciPost Physics, Vol. 6, Issue 4
Axial anomalies and index theorems on open spaces
journal, October 1978
- Callias, Constantine
- Communications in Mathematical Physics, Vol. 62, Issue 3
Sigma models on flags
journal, January 2019
- Ohmori, Kantaro; Seiberg, Nathan; Shao, Shu-Heng
- SciPost Physics, Vol. 6, Issue 2
Some remarks on the paper of Callias
journal, October 1978
- Bott, R.; Seeley, R.
- Communications in Mathematical Physics, Vol. 62, Issue 3
Three-dimensional dualities with bosons and fermions
journal, February 2018
- Benini, Francesco
- Journal of High Energy Physics, Vol. 2018, Issue 2
Anomalies involving the space of couplings and the Zamolodchikov metric
journal, December 2017
- Tachikawa, Yuji
- Journal of High Energy Physics, Vol. 2017, Issue 12
Shortening anomalies in supersymmetric theories
journal, January 2017
- Gomis, Jaume; Komargodski, Zohar; Ooguri, Hirosi
- Journal of High Energy Physics, Vol. 2017, Issue 1
Anomaly and global inconsistency matching: angles, nonlinear sigma model, chains, and generalizations
journal, September 2018
- Tanizaki, Yuya; Sulejmanpasic, Tin
- Physical Review B, Vol. 98, Issue 11
Chern-Simons-matter dualities with SO and USp gauge groups
journal, February 2017
- Aharony, Ofer; Benini, Francesco; Hsin, Po-Shen
- Journal of High Energy Physics, Vol. 2017, Issue 2
Exploring 2-group global symmetries
journal, February 2019
- Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
- Journal of High Energy Physics, Vol. 2019, Issue 2