Vacuum structure of Yang-Mills theory as a function of θ
Abstract
It is believed that in SU(N) Yang-Mills theory observables are N -branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of θ. We study the number of θ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on $$ \mathbb{R}$$3 × S1. We find that while observables are indeed N-branched functions of θ, there are only ≈ N/2 locally-stable candidate vacua for any given θ. We point out that the different θ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero ’t Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of θ, and gather evidence for the conjecture that these spinodal points are present even in the $$ \mathbb{R}$$4 limit.
- Authors:
-
- Univ. of Washington, Seattle, WA (United States). Dept. of Physics
- Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory
- North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Univ. of Washington, Seattle, WA (United States); North Carolina State University, Raleigh, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1507783
- Grant/Contract Number:
- FG02-00ER41132; FG02-03ER41260; SC0011637
- 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: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Discrete Symmetries, Global Symmetries, Spontaneous Symmetry Breaking, Wilson, 't Hooft and Polyakov loops
Citation Formats
Aitken, Kyle, Cherman, Aleksey, and Ünsal, Mithat. Vacuum structure of Yang-Mills theory as a function of θ. United States: N. p., 2018.
Web. doi:10.1007/jhep09(2018)030.
Aitken, Kyle, Cherman, Aleksey, & Ünsal, Mithat. Vacuum structure of Yang-Mills theory as a function of θ. United States. https://doi.org/10.1007/jhep09(2018)030
Aitken, Kyle, Cherman, Aleksey, and Ünsal, Mithat. Thu .
"Vacuum structure of Yang-Mills theory as a function of θ". United States. https://doi.org/10.1007/jhep09(2018)030. https://www.osti.gov/servlets/purl/1507783.
@article{osti_1507783,
title = {Vacuum structure of Yang-Mills theory as a function of θ},
author = {Aitken, Kyle and Cherman, Aleksey and Ünsal, Mithat},
abstractNote = {It is believed that in SU(N) Yang-Mills theory observables are N -branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of θ. We study the number of θ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on $ \mathbb{R}$3 × S1. We find that while observables are indeed N-branched functions of θ, there are only ≈ N/2 locally-stable candidate vacua for any given θ. We point out that the different θ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero ’t Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of θ, and gather evidence for the conjecture that these spinodal points are present even in the $ \mathbb{R}$4 limit.},
doi = {10.1007/jhep09(2018)030},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2018,
place = {United States},
year = {Thu Sep 06 00:00:00 EDT 2018},
month = {Thu Sep 06 00:00:00 EDT 2018}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Order Parameters and Color-Flavor Center Symmetry in QCD
journal, November 2017
- Cherman, Aleksey; Sen, Srimoyee; Ünsal, Mithat
- Physical Review Letters, Vol. 119, Issue 22
Sign problem in a -symmetric effective Polyakov-line model
journal, October 2017
- Hirakida, Takehiro; Sugano, Junpei; Kouno, Hiroaki
- Physical Review D, Vol. 96, Issue 7
Gluino condensate and magnetic monopoles in supersymmetric gluodynamics
journal, October 1999
- Davies, N. Michael; Hollowood, Timothy J.; Khoze, Valentin V.
- Nuclear Physics B, Vol. 559, Issue 1-2
θ dependence of SU(N) gauge theories in the presence of a topological term
journal, January 2009
- Vicari, Ettore; Panagopoulos, Haralambos
- Physics Reports, Vol. 470, Issue 3-4
Theta Dependence in the Large Limit of Four-Dimensional Gauge Theories
journal, October 1998
- Witten, Edward
- Physical Review Letters, Vol. 81, Issue 14
Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory
journal, January 2008
- Ünsal, Mithat
- Physical Review Letters, Vol. 100, Issue 3
Gauge theories and magnetic charge
journal, July 1977
- Goddard, P.; Nuyts, J.; Olive, D.
- Nuclear Physics B, Vol. 125, Issue 1
Theta, time reversal and temperature
journal, May 2017
- Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
- Journal of High Energy Physics, Vol. 2017, Issue 5
Theta, Time Reversal, and Temperature
text, January 2017
- Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar
- arXiv
Differences and similarities between fundamental and adjoint matters in gauge theories
journal, July 2013
- Kouno, Hiroaki; Misumi, Tatsuhiro; Kashiwa, Kouji
- Physical Review D, Vol. 88, Issue 1
Black hole portal into hidden valleys
journal, May 2011
- Dubovsky, Sergei; Gorbenko, Victor
- Physical Review D, Vol. 83, Issue 10
Quark–gluon thermodynamics with the ${Z}_{N_c}$ symmetry
journal, July 2012
- Kouno, Hiroaki; Sakai, Yuji; Makiyama, Takahiro
- Journal of Physics G: Nuclear and Particle Physics, Vol. 39, Issue 8
Center-stabilized Yang-Mills theory: Confinement and large volume independence
journal, September 2008
- Ünsal, Mithat; Yaffe, Laurence G.
- Physical Review D, Vol. 78, Issue 6
Polyakov loops and the Hosotani mechanism on the lattice
journal, May 2014
- Cossu, Guido; Noaki, Jun-Ichi; Hatanaka, Hisaki
- Physical Review D, Vol. 89, Issue 9
Exponential reduction of finite volume effects with twisted boundary conditions
journal, April 2017
- Cherman, Aleksey; Sen, Srimoyee; Wagman, Michael L.
- Physical Review D, Vol. 95, Issue 7
Understanding QCD at high density from a -symmetric QCD-like theory
journal, March 2016
- Kouno, Hiroaki; Kashiwa, Kouji; Takahashi, Junichi
- Physical Review D, Vol. 93, Issue 5
Topological susceptibility and contact term in QCD: A toy model
journal, February 2012
- Thomas, Evan; Zhitnitsky, Ariel R.
- Physical Review D, Vol. 85, Issue 4
Semiclassical Realization of Infrared Renormalons
journal, September 2012
- Argyres, Philip; Ünsal, Mithat
- Physical Review Letters, Vol. 109, Issue 12
Phase diagram of Yang-Mills theories in the presence of a term
journal, August 2013
- D’Elia, Massimo; Negro, Francesco
- Physical Review D, Vol. 88, Issue 3
The quarkyonic phase and the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:math> symmetry
journal, November 2012
- Sakai, Yuji; Kouno, Hiroaki; Sasaki, Takahiro
- Physics Letters B, Vol. 718, Issue 1
Current algebra theorems for the U(1) “Goldstone boson”
journal, September 1979
- Witten, E.
- Nuclear Physics B, Vol. 156, Issue 2
Confinement and $\mathbb {Z}_{3}$ symmetry in three-flavor QCD
journal, August 2013
- Kouno, Hiroaki; Makiyama, Takahiro; Sasaki, Takahiro
- Journal of Physics G: Nuclear and Particle Physics, Vol. 40, Issue 9
Lattice study on QCD-like theory with exact center symmetry
journal, November 2015
- Iritani, Takumi; Itou, Etsuko; Misumi, Tatsuhiro
- Journal of High Energy Physics, Vol. 2015, Issue 11
Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups
journal, March 2013
- Poppitz, Erich; Schäfer, Thomas; Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2013, Issue 3
Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD
journal, July 2015
- Anber, Mohamed M.; Poppitz, Erich; Sulejmanpašić, Tin
- Physical Review D, Vol. 92, Issue 2
Adjoint QCD on ℝ3 × S 1 with twisted fermionic boundary conditions
journal, June 2014
- Misumi, Tatsuhiro; Kanazawa, Takuya
- Journal of High Energy Physics, Vol. 2014, Issue 6
Interplay between sign problem and symmetry in three-dimensional Potts models
journal, July 2016
- Hirakida, Takehiro; Kouno, Hiroaki; Takahashi, Junichi
- Physical Review D, Vol. 94, Issue 1
Dependence of the Deconfinement Temperature in Yang-Mills Theories
journal, August 2012
- D’Elia, Massimo; Negro, Francesco
- Physical Review Letters, Vol. 109, Issue 7
Oblique confinement at in weakly coupled gauge theories with deformations
journal, October 2017
- Anber, Mohamed M.; Zhitnitsky, Ariel R.
- Physical Review D, Vol. 96, Issue 7
Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups
text, January 2012
- Poppitz, Erich; Schaefer, Thomas; Unsal, Mithat
- arXiv
Seiberg-Witten and “Polyakov-like” magnetic bion confinements are continuously connected
journal, July 2011
- Poppitz, Erich; Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2011, Issue 7
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
text, January 2012
- Argyres, Philip C.; Ünsal, Mithat
- arXiv
Monopoles and instantons on partially compactified -branes
journal, September 1997
- Lee, Kimyeong; Yi, Piljin
- Physical Review D, Vol. 56, Issue 6
Monopoles, affine algebras and the gluino condensate
journal, August 2003
- Davies, N. Michael; Hollowood, Timothy J.; Khoze, Valentin V.
- Journal of Mathematical Physics, Vol. 44, Issue 8
Finite size phase transitions in QCD with adjoint fermions
text, January 2009
- Cossu, Guido; D'Elia, Massimo
- arXiv
Coupling a QFT to a TQFT and duality
journal, April 2014
- Kapustin, Anton; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2014, Issue 4
Change of Dependence in 4D Gauge Theories Across the Deconfinement Transition
journal, June 2013
- Bonati, Claudio; D’Elia, Massimo; Panagopoulos, Haralambos
- Physical Review Letters, Vol. 110, Issue 25
Compactified N = 1 $$ \mathcal{N}=1 $$ supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition
journal, December 2014
- Bergner, G.; Piemonte, S.
- Journal of High Energy Physics, Vol. 2014, Issue 12
Hidden Topological Angles in Path Integrals
journal, July 2015
- Behtash, Alireza; Sulejmanpasic, Tin; Schäfer, Thomas
- Physical Review Letters, Vol. 115, Issue 4
New nonperturbative scales and glueballs in confining supersymmetric gauge theories
journal, March 2018
- Anber, Mohamed M.; Poppitz, Erich
- Journal of High Energy Physics, Vol. 2018, Issue 3
Axion monodromy in a model of holographic gluodynamics
journal, February 2012
- Dubovsky, Sergei; Lawrence, Albion; Roberts, Matthew M.
- Journal of High Energy Physics, Vol. 2012, Issue 2
A semiclassical realization of infrared renormalons
text, January 2012
- Argyres, Philip; Unsal, Mithat
- arXiv
A expandable series of non-linear σ models with instantons
journal, December 1978
- D'Adda, A.; Lüscher, M.; Di Vecchia, P.
- Nuclear Physics B, Vol. 146, Issue 1
Continuity, deconfinement, and (super) Yang-Mills theory
journal, October 2012
- Poppitz, Erich; Schäfer, Thomas; Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2012, Issue 10
Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories
text, January 1998
- Witten, Edward
- arXiv
Instatons, the quark model, and the 1/N expansion
journal, March 1979
- Witten, Edward
- Nuclear Physics B, Vol. 149, Issue 2
Lattice study on QCD-like theory with exact center symmetry
text, January 2015
- Iritani, Takumi; Itou, Etsuko; Misumi, Tatsuhiro
- arXiv
Metastable vacuum decay and θ dependence in gauge theory. Deformed QCD as a toy model
journal, January 2015
- Bhoonah, Amit; Thomas, Evan; Zhitnitsky, Ariel R.
- Nuclear Physics B, Vol. 890
Theta dependence, sign problems, and topological interference
journal, November 2012
- Ünsal, Mithat
- Physical Review D, Vol. 86, Issue 10
Monopoles, affine algebras and the gluino condensate
text, January 2000
- Davies, N. Michael; Hollowood, Timothy J.; Khoze, Valentin V.
- arXiv
Deconfinement in $ \mathcal{N}=1 $ super Yang-Mills theory on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ via dual-Coulomb gas and “affine” XY-model
journal, November 2013
- Anber, Mohamed M.; Collier, Scott; Poppitz, Erich
- Journal of High Energy Physics, Vol. 2013, Issue 11
Emergent dimensions and branes from large- confinement
journal, December 2016
- Cherman, Aleksey; Poppitz, Erich
- Physical Review D, Vol. 94, Issue 12
Are there monopoles in the quark-gluon plasma?
journal, June 2018
- Ramamurti, Adith; Shuryak, Edward; Zahed, Ismail
- Physical Review D, Vol. 97, Issue 11
Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
journal, September 2009
- Ünsal, Mithat
- Physical Review D, Vol. 80, Issue 6
dependence of 4D gauge theories in the large- limit
journal, October 2016
- Bonati, Claudio; D’Elia, Massimo; Rossi, Paolo
- Physical Review D, Vol. 94, Issue 8
Continuity, Deconfinement, and (Super) Yang-Mills Theory
text, January 2012
- Poppitz, Erich; Schaefer, Thomas; Unsal, Mithat
- arXiv
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
journal, August 2012
- Argyres, Philip C.; Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2012, Issue 8
Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
text, January 2014
- Anber, Mohamed M.; Poppitz, Erich; Teeple, Brett
- arXiv
Domain walls and the decay rate of the excited vacua in large Yang-Mills theory
journal, December 1998
- Shifman, M.
- Physical Review D, Vol. 59, Issue 2
Periodic instantons with non-trivial holonomy
journal, November 1998
- Kraan, Thomas C.; van Baal, Pierre
- Nuclear Physics B, Vol. 533, Issue 1-3
The 4D SU(3) gauge theory with an imaginary θ term
journal, November 2011
- Panagopoulos, Haralambos; Vicari, Ettore
- Journal of High Energy Physics, Vol. 2011, Issue 11
Notes on theta dependence in holographic Yang-Mills
journal, August 2015
- Bigazzi, Francesco; Cotrone, Aldo L.; Sisca, Roberto
- Journal of High Energy Physics, Vol. 2015, Issue 8
Microscopic structure of magnetic bions
journal, June 2011
- Anber, Mohamed M.; Poppitz, Erich
- Journal of High Energy Physics, Vol. 2011, Issue 6
Thermal properties of gauge fields and quark liberation
journal, January 1978
- Polyakov, A. M.
- Physics Letters B, Vol. 72, Issue 4
Finite size phase transitions in QCD with adjoint fermions
journal, July 2009
- Cossu, Guido; D'Elia, Massimo
- Journal of High Energy Physics, Vol. 2009, Issue 07
Quark masses and chiral symmetry
journal, September 1995
- Creutz, Michael
- Physical Review D, Vol. 52, Issue 5
Notes on Theta Dependence in Holographic Yang-Mills
text, January 2015
- Bigazzi, Francesco; Cotrone, Aldo L.; Sisca, Roberto
- arXiv
Metastable vacuum decay in center-stabilized Yang-Mills theory at large
journal, November 2014
- Li, Xin; Voloshin, M. B.
- Physical Review D, Vol. 90, Issue 10
θ and the η ′ in large N supersymmetric QCD
journal, May 2017
- Dine, Michael; Draper, Patrick; Stephenson-Haskins, Laurel
- Journal of High Energy Physics, Vol. 2017, Issue 5
θ dependence of SU( N ) gauge theories
journal, August 2002
- Debbio, Luigi Del; Panagopoulos, Haralambos; Vicari, Ettore
- Journal of High Energy Physics, Vol. 2002, Issue 08
QCD-like theories on : A smooth journey from small to large with double-trace deformations
journal, September 2008
- Shifman, M.; Ünsal, Mithat
- Physical Review D, Vol. 78, Issue 6
Yang-Mills theories with chiral matter at strong coupling
journal, May 2009
- Shifman, M.; Ünsal, Mithat
- Physical Review D, Vol. 79, Issue 10
Phase diagrams of SU( N ) gauge theories with fermions in various representations
journal, July 2009
- Myers, Joyce C.; Ogilvie, Michael C.
- Journal of High Energy Physics, Vol. 2009, Issue 07
Deconfinement in Yang-Mills theory through toroidal compactification with deformation
journal, May 2012
- Simić, Dušan; Ünsal, Mithat
- Physical Review D, Vol. 85, Issue 10
Large-N volume independence in conformal and confining gauge theories
journal, August 2010
- Ünsal, Mithat; Yaffe, Laurence G.
- Journal of High Energy Physics, Vol. 2010, Issue 8
2d affine XY-spin model/4d gauge theory duality and deconfinement
journal, April 2012
- Anber, Mohamed M.; Poppitz, Erich; Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2012, Issue 4
On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ 3 × S 1 $$ {\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}^1 $$
journal, October 2015
- Anber, Mohamed M.; Poppitz, Erich
- Journal of High Energy Physics, Vol. 2015, Issue 10
Classification of compactified su(Nc) gauge theories with fermions in all representations
journal, December 2017
- Anber, Mohamed M.; Vincent-Genod, Loïc
- Journal of High Energy Physics, Vol. 2017, Issue 12
On the phase transition towards permanent quark confinement
journal, June 1978
- 't Hooft, G.
- Nuclear Physics B, Vol. 138, Issue 1
An Elliptic Superpotential for Softly Broken Script N = 4 Supersymmetric Yang-Mills Theory
journal, July 1999
- Dorey, Nick
- Journal of High Energy Physics, Vol. 1999, Issue 07
String tensions in deformed Yang-Mills theory
journal, January 2018
- Poppitz, Erich; Shalchian T., M. Erfan
- Journal of High Energy Physics, Vol. 2018, Issue 1
Confinement in the Bulk, Deconfinement on the Wall: Infrared Equivalence between Compactified QCD and Quantum Magnets
journal, September 2017
- Sulejmanpasic, Tin; Shao, Hui; Sandvik, Anders W.
- Physical Review Letters, Vol. 119, Issue 9
Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
journal, September 2014
- Anber, Mohamed M.; Poppitz, Erich; Teeple, Brett
- Journal of High Energy Physics, Vol. 2014, Issue 9
Free energy and θ dependence of SU(N) gauge theories
journal, May 2003
- Del Debbio, L.; Panagopoulos, H.; Vicari, E.
- Nuclear Physics B - Proceedings Supplements, Vol. 119
Large- reduction in QCD-like theories with massive adjoint fermions
journal, December 2010
- Azeyanagi, Tatsuo; Hanada, Masanori; Ünsal, Mithat
- Physical Review D, Vol. 82, Issue 12
Representation dependence of -strings in pure Yang-Mills theory via supersymmetry
journal, December 2017
- Anber, Mohamed M.; Pellizzani, Vito
- Physical Review D, Vol. 96, Issue 11
Phase transitions in center-stabilized lattice gauge theories
conference, July 2012
- Vairinhos, Helvio
- Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)
A semiclassical realization of infrared renormalons
text, January 2012
- Argyres, Philip; Unsal, Mithat
- arXiv
Differences and similarities between fundamental and adjoint matters in SU(N) gauge theories
text, January 2013
- Kouno, Hiroaki; Misumi, Tatsuhiro; Kashiwa, Kouji
- arXiv
Hidden topological angles and Lefschetz thimbles
text, January 2015
- Behtash, Alireza; Sulejmanpasic, Tin; Schaefer, Thomas
- arXiv
Lattice study on QCD-like theory with exact center symmetry
text, January 2015
- Iritani, Takumi; Itou, Etsuko; Misumi, Tatsuhiro
- arXiv
Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model
text, January 2016
- Hirakida, Takehiro; Kouno, Hiroaki; Takahashi, Junichi
- arXiv
Works referencing / citing this record:
QCD domain walls, Chern-Simons theories and holography
journal, September 2018
- Argurio, Riccardo; Bertolini, Matteo; Bigazzi, Francesco
- Journal of High Energy Physics, Vol. 2018, Issue 9
Do we live in the swampland?
journal, December 2018
- Murayama, Hitoshi; Yamazaki, Masahito; Yanagida, Tsutomu T.
- Journal of High Energy Physics, Vol. 2018, Issue 12
Dihedral symmetry in Yang-Mills theory
journal, October 2019
- Aitken, Kyle; Cherman, Aleksey; Ünsal, Mithat
- Physical Review D, Vol. 100, Issue 8
Figures / Tables found in this record: