Anomalies in the space of coupling constants and their dynamical applications II
Abstract
We extend our earlier work on anomalies in the space of coupling constants to fourdimensional gauge theories. Pure YangMills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its oneform global symmetry (associated with the center) and the periodicity of the \theta $\theta $ parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as timereversal). We also study SU(N) $SU\left(N\right)$ and Sp(N) $Sp\left(N\right)$ gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the \theta $\theta $ periodicity. Again, this anomaly unifies distinct recentlydiscovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.
 Authors:

 Institute for Advanced Study, Princeton University
 The University of Texas at Austin
 Princeton University
 Publication Date:
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1581450
 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 25424653
 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 II. Netherlands: N. p., 2020.
Web. doi:10.21468/SciPostPhys.8.1.002.
Cordova, Clay, Freed, Daniel, Lam, Ho Tat, & Seiberg, Nathan. Anomalies in the space of coupling constants and their dynamical applications II. Netherlands. doi:10.21468/SciPostPhys.8.1.002.
Cordova, Clay, Freed, Daniel, Lam, Ho Tat, and Seiberg, Nathan. Tue .
"Anomalies in the space of coupling constants and their dynamical applications II". Netherlands. doi:10.21468/SciPostPhys.8.1.002.
@article{osti_1581450,
title = {Anomalies in the space of coupling constants and their dynamical applications II},
author = {Cordova, Clay and Freed, Daniel and Lam, Ho Tat and Seiberg, Nathan},
abstractNote = {We extend our earlier work on anomalies in the space of coupling constants to fourdimensional gauge theories. Pure YangMills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its oneform global symmetry (associated with the center) and the periodicity of the \theta θ parameter. This anomaly is at the root of many recently discovered properties of these theories, including their phase transitions and interfaces. These new anomalies can be used to extend this understanding to systems without discrete symmetries (such as timereversal). We also study SU(N) S U ( N ) and Sp(N) S p ( N ) gauge theories with matter in the fundamental representation. Here we find a mixed anomaly between the flavor symmetry group and the \theta θ periodicity. Again, this anomaly unifies distinct recentlydiscovered phenomena in these theories and controls phase transitions and the dynamics on interfaces.},
doi = {10.21468/SciPostPhys.8.1.002},
journal = {SciPost Physics Proceedings},
number = 1,
volume = 8,
place = {Netherlands},
year = {2020},
month = {1}
}
DOI: 10.21468/SciPostPhys.8.1.002
Web of Science
Works referenced in this record:
Order Parameters and ColorFlavor Center Symmetry in QCD
journal, November 2017
 Cherman, Aleksey; Sen, Srimoyee; Ünsal, Mithat
 Physical Review Letters, Vol. 119, Issue 22
On 2group global symmetries and their anomalies
journal, March 2019
 Benini, Francesco; Córdova, Clay; Hsin, PoShen
 Journal of High Energy Physics, Vol. 2019, Issue 3
Anomaly matching in QCD thermal phase transition
journal, May 2019
 Yonekura, Kazuya
 Journal of High Energy Physics, Vol. 2019, Issue 5
Theta, time reversal and temperature
journal, May 2017
 Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
 Journal of High Energy Physics, Vol. 2017, Issue 5
Some Features of Chiral Symmetry Breaking
journal, April 1971
 Dashen, Roger
 Physical Review D, Vol. 3, Issue 8
Comments on oneform global symmetries and their gauging in 3d and 4d
journal, January 2019
 Hsin, PoShen; Lam, Ho Tat; Seiberg, Nathan
 SciPost Physics, Vol. 6, 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 14
Dbrane charges in fivebrane backgrounds
journal, October 2001
 Maldacena, Juan; Seiberg, Nathan; Moore, Gregory
 Journal of High Energy Physics, Vol. 2001, Issue 10
Symmetries and strings in field theory and gravity
journal, April 2011
 Banks, Tom; Seiberg, Nathan
 Physical Review D, Vol. 83, Issue 8
Topological order in the colorflavor locked phase of a ( 3 + 1 )dimensional U ( N ) gaugeHiggs system
journal, December 2019
 Hidaka, Yoshimasa; Hirono, Yuji; Nitta, Muneto
 Physical Review D, Vol. 100, Issue 12
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; SchäferNameki, Sakura
 Journal of High Energy Physics, Vol. 2018, Issue 10
Timereversal 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 highT SU(N) super YangMills theory and QCD(adj)
journal, May 2019
 Anber, Mohamed M.; Poppitz, Erich
 Journal of High Energy Physics, Vol. 2019, Issue 5
Timereversal symmetry, anomalies, and dualities in (2+1)$d$
journal, January 2018
 Cordova, Clay; Hsin, PoShen; Seiberg, Nathan
 SciPost Physics, Vol. 5, Issue 1
A computation of Tr(−1)F in supersymmetric gauge theories with matter
journal, August 1983
 Cohen, Eyal; Gomez, Cesar
 Nuclear Physics B, Vol. 223, Issue 1
Relative Quantum Field Theory
journal, January 2014
 Freed, Daniel S.; Teleman, Constantin
 Communications in Mathematical Physics, Vol. 326, Issue 2
Anomaly matching for the phase diagram of massless ${\mathbb{Z}}_{N}$ QCD
journal, March 2018
 Tanizaki, Yuya; Kikuchi, Yuta; Misumi, Tatsuhiro
 Physical Review D, Vol. 97, Issue 5
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
Exceptional ChernSimonsMatter dualities
journal, January 2019
 Cordova, Clay; Hsin, PoShen; Ohmori, Kantaro
 SciPost Physics, Vol. 7, Issue 4
Coupling a QFT to a TQFT and duality
journal, April 2014
 Kapustin, Anton; Seiberg, Nathan
 Journal of High Energy Physics, Vol. 2014, Issue 4
Algebraic and Hamiltonian methods in the theory of nonAbelian anomalies
journal, August 1984
 Faddeev, L. D.; Shatashvili, S. L.
 Theoretical and Mathematical Physics, Vol. 60, Issue 2
The bifundamental 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
Reading between the lines of fourdimensional gauge theories
journal, August 2013
 Aharony, Ofer; Seiberg, Nathan; Tachikawa, Yuji
 Journal of High Energy Physics, Vol. 2013, Issue 8
Quantum 4d YangMills theory and timereversal symmetric 5d highergauge topological field theory
journal, October 2019
 Wan, Zheyan; Wang, Juven; Zheng, Yunqin
 Physical Review D, Vol. 100, Issue 8
A expandable series of nonlinear σ models with instantons
journal, December 1978
 D'Adda, A.; Lüscher, M.; Di Vecchia, P.
 Nuclear Physics B, Vol. 146, Issue 1
A symmetry breaking scenario for QCD3
journal, January 2018
 Komargodski, Zohar; Seiberg, Nathan
 Journal of High Energy Physics, Vol. 2018, Issue 1
More about the massive Schwinger model
journal, September 1976
 Coleman, Sidney
 Annals of Physics, Vol. 101, Issue 1
$\mathrm{CP}$ nonconserving effects in quantum chromodynamics
journal, April 1979
 Baluni, Varouzhan
 Physical Review D, Vol. 19, Issue 7
Instatons, the quark model, and the 1/N expansion
journal, March 1979
 Witten, Edward
 Nuclear Physics B, Vol. 149, Issue 2
Anomaly of the Electromagnetic Duality of Maxwell Theory
journal, October 2019
 Hsieh, ChangTse; Tachikawa, Yuji; Yonekura, Kazuya
 Physical Review Letters, Vol. 123, Issue 16
Comments on global symmetries, anomalies, and duality in (2 + 1)d
journal, April 2017
 Benini, Francesco; Hsin, PoShen; 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
A duality web in $2+1$ dimensions and condensed matter physics
journal, November 2016
 Seiberg, Nathan; Senthil, T.; Wang, Chong
 Annals of Physics, Vol. 374
Characteristic Classes and Homogeneous Spaces, I
journal, April 1958
 Borel, A.; Hirzebruch, F.
 American Journal of Mathematics, Vol. 80, Issue 2
Level/rank duality and ChernSimonsmatter theories
journal, September 2016
 Hsin, PoShen; Seiberg, Nathan
 Journal of High Energy Physics, Vol. 2016, Issue 9
Circle compactification and ’t Hooft anomaly
journal, December 2017
 Tanizaki, Yuya; Misumi, Tatsuhiro; Sakai, Norisuke
 Journal of High Energy Physics, Vol. 2017, Issue 12
Anomaly constraints on deconfinement and chiral phase transition
journal, May 2018
 Shimizu, Hiroyuki; Yonekura, Kazuya
 Physical Review D, Vol. 97, Issue 10
A property of electric and magnetic flux in nonAbelian gauge theories
journal, January 1979
 't Hooft, G.
 Nuclear Physics B, Vol. 153
Global Symmetries, Counterterms, and Duality in ChernSimons Matter Theories with Orthogonal Gauge Groups
journal, January 2018
 Cordova, Clay; Hsin, PoShen; Seiberg, Nathan
 SciPost Physics, Vol. 4, Issue 4
Supersymmetric index in fourdimensional gauge theories
journal, January 2001
 Witten, Edward
 Advances in Theoretical and Mathematical Physics, Vol. 5, 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 superQCD
journal, January 2019
 Bashmakov, Vladimir; Benini, Francesco; Benvenuti, Sergio
 SciPost Physics, Vol. 6, Issue 4
Threedimensional 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
ChernSimonsmatter dualities with SO and USp gauge groups
journal, February 2017
 Aharony, Ofer; Benini, Francesco; Hsin, PoShen
 Journal of High Energy Physics, Vol. 2017, Issue 2
Current algebra, baryons, and quark confinement
journal, August 1983
 Witten, Edward
 Nuclear Physics B, Vol. 223, Issue 2
Exploring 2group global symmetries
journal, February 2019
 Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
 Journal of High Energy Physics, Vol. 2019, Issue 2