Vacuum structure of Yang-Mills theory as a function of θ

Aitken, Kyle; Cherman, Aleksey; Ünsal, Mithat

doi:10.1007/jhep09(2018)030

Title: 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:

Aitken, Kyle ^[1]; Cherman, Aleksey ^[2]; Ünsal, Mithat ^[3]

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:: 2018-09-06

Research Org.:: Univ. of Washington, Seattle, WA (United States); North Carolina State Univ., 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.

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                    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

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                    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.

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@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         = {2018},

  month        = {9}

}

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Figure 1: [Color Online.] An sketch of the phase structure of SU(N) YM theory for N = 4 as a function of θ. The vertical axis depicts the vacuum energy density. The gray dashed curves indicate the energy density associated with the four distinct θ-extrema. The colored bold curves indicatemore »

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Works referencing / citing this record:

QCD domain walls, Chern-Simons theories and holography
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Title: Vacuum structure of Yang-Mills theory as a function of θ

Abstract

Citation Formats

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Current algebra theorems for the U(1) “Goldstone boson” journal, September 1979

Confinement and $\mathbb {Z}_{3}$ symmetry in three-flavor QCD journal, August 2013

Lattice study on QCD-like theory with exact center symmetry journal, November 2015

Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups journal, March 2013

Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups journal, September 2014

Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD journal, July 2015

Adjoint QCD on ℝ3 × S 1 with twisted fermionic boundary conditions journal, June 2014

Interplay between sign problem and Z 3 symmetry in three-dimensional Potts models journal, July 2016

θ Dependence of the Deconfinement Temperature in Yang-Mills Theories journal, August 2012

Large- N reduction in QCD-like theories with massive adjoint fermions journal, December 2010

Oblique confinement at θ ≠ 0 in weakly coupled gauge theories with deformations journal, October 2017

Seiberg-Witten and “Polyakov-like” magnetic bion confinements are continuously connected journal, July 2011

Large N chiral dynamics journal, September 1980

Monopoles and instantons on partially compactified D -branes journal, September 1997

Monopoles, affine algebras and the gluino condensate journal, August 2003

Coupling a QFT to a TQFT and duality journal, April 2014

Change of θ Dependence in 4D SU ( N ) Gauge Theories Across the Deconfinement Transition journal, June 2013

Compactified N = 1 $$ \mathcal{N}=1 $$ supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition journal, December 2014

Dyons of charge eθ/2π journal, October 1979

Hidden Topological Angles in Path Integrals journal, July 2015

New nonperturbative scales and glueballs in confining supersymmetric gauge theories journal, March 2018

Axion monodromy in a model of holographic gluodynamics journal, February 2012

A expandable series of non-linear σ models with instantons journal, December 1978

Continuity, deconfinement, and (super) Yang-Mills theory journal, October 2012

Instatons, the quark model, and the 1/N expansion journal, March 1979

Metastable vacuum decay and θ dependence in gauge theory. Deformed QCD as a toy model journal, January 2015

Theta dependence, sign problems, and topological interference journal, November 2012

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

Emergent dimensions and branes from large- N confinement journal, December 2016

Are there monopoles in the quark-gluon plasma? journal, June 2018

Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions journal, September 2009

θ dependence of 4D S U ( N ) gauge theories in the large- N limit journal, October 2016

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects journal, August 2012

Domain walls and the decay rate of the excited vacua in large N Yang-Mills theory journal, December 1998

Periodic instantons with non-trivial holonomy journal, November 1998

The 4D SU(3) gauge theory with an imaginary θ term journal, November 2011

Notes on theta dependence in holographic Yang-Mills journal, August 2015

Microscopic structure of magnetic bions journal, June 2011

Thermal properties of gauge fields and quark liberation journal, January 1978

Finite size phase transitions in QCD with adjoint fermions journal, July 2009

Quark masses and chiral symmetry journal, September 1995

Metastable vacuum decay in center-stabilized Yang-Mills theory at large N journal, November 2014

QCD domain walls, Chern-Simons theories and holography journal, September 2018

Do we live in the swampland? journal, December 2018

Dihedral symmetry in S U ( N ) Yang-Mills theory journal, October 2019

Representation dependence of $k$ -strings in pure Yang-Mills theory via supersymmetry
journal, December 2017

Order Parameters and Color-Flavor Center Symmetry in QCD
journal, November 2017

Sign problem in a $Z_{3}$ -symmetric effective Polyakov-line model
journal, October 2017

Gluino condensate and magnetic monopoles in supersymmetric gluodynamics
journal, October 1999

θ dependence of SU(N) gauge theories in the presence of a topological term
journal, January 2009

Theta Dependence in the Large $N$ Limit of Four-Dimensional Gauge Theories
journal, October 1998

Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory
journal, January 2008

Gauge theories and magnetic charge
journal, July 1977

Theta, time reversal and temperature
journal, May 2017

QCD on a small circle
journal, November 2017

Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
journal, August 2016

Differences and similarities between fundamental and adjoint matters in $S U (N)$ gauge theories
journal, July 2013

Black hole portal into hidden valleys
journal, May 2011

Quark–gluon thermodynamics with the ${Z}_{N_c}$ symmetry
journal, July 2012

Center-stabilized Yang-Mills theory: Confinement and large $N$ volume independence
journal, September 2008

Polyakov loops and the Hosotani mechanism on the lattice
journal, May 2014

Exponential reduction of finite volume effects with twisted boundary conditions
journal, April 2017

Understanding QCD at high density from a $Z_{3}$ -symmetric QCD-like theory
journal, March 2016

Topological susceptibility and contact term in QCD: A toy model
journal, February 2012

Semiclassical Realization of Infrared Renormalons
journal, September 2012

Phase diagram of Yang-Mills theories in the presence of a $θ$ term
journal, August 2013

QCD at $θ \sim π$
journal, May 1999

Current algebra theorems for the U(1) “Goldstone boson”
journal, September 1979

Confinement and $\mathbb {Z}_{3}$ symmetry in three-flavor QCD
journal, August 2013

Lattice study on QCD-like theory with exact center symmetry
journal, November 2015

Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups
journal, March 2013

Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
journal, September 2014

Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD
journal, July 2015

Adjoint QCD on ℝ3 × S 1 with twisted fermionic boundary conditions
journal, June 2014

Interplay between sign problem and $Z_{3}$ symmetry in three-dimensional Potts models
journal, July 2016

$θ$ Dependence of the Deconfinement Temperature in Yang-Mills Theories
journal, August 2012

Large- $N$ reduction in QCD-like theories with massive adjoint fermions
journal, December 2010

Oblique confinement at $θ \neq 0$ in weakly coupled gauge theories with deformations
journal, October 2017

Seiberg-Witten and “Polyakov-like” magnetic bion confinements are continuously connected
journal, July 2011

Large N chiral dynamics
journal, September 1980

Monopoles and instantons on partially compactified $D$ -branes
journal, September 1997

Monopoles, affine algebras and the gluino condensate
journal, August 2003

Coupling a QFT to a TQFT and duality
journal, April 2014

Change of $θ$ Dependence in 4D $SU (N)$ Gauge Theories Across the Deconfinement Transition
journal, June 2013

Compactified N = 1 $$ \mathcal{N}=1 $$ supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition
journal, December 2014

Dyons of charge eθ/2π
journal, October 1979

Hidden Topological Angles in Path Integrals
journal, July 2015

New nonperturbative scales and glueballs in confining supersymmetric gauge theories
journal, March 2018

Axion monodromy in a model of holographic gluodynamics
journal, February 2012

A expandable series of non-linear σ models with instantons
journal, December 1978

Continuity, deconfinement, and (super) Yang-Mills theory
journal, October 2012

Instatons, the quark model, and the 1/N expansion
journal, March 1979

Metastable vacuum decay and θ dependence in gauge theory. Deformed QCD as a toy model
journal, January 2015

Theta dependence, sign problems, and topological interference
journal, November 2012

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

Emergent dimensions and branes from large- $N$ confinement
journal, December 2016

Are there monopoles in the quark-gluon plasma?
journal, June 2018

Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
journal, September 2009

$θ$ dependence of 4D $S U (N)$ gauge theories in the large- $N$ limit
journal, October 2016

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
journal, August 2012

Domain walls and the decay rate of the excited vacua in large $N$ Yang-Mills theory
journal, December 1998

Periodic instantons with non-trivial holonomy
journal, November 1998

The 4D SU(3) gauge theory with an imaginary θ term
journal, November 2011

Notes on theta dependence in holographic Yang-Mills
journal, August 2015

Microscopic structure of magnetic bions
journal, June 2011

Thermal properties of gauge fields and quark liberation
journal, January 1978

Finite size phase transitions in QCD with adjoint fermions
journal, July 2009

Quark masses and chiral symmetry
journal, September 1995

Metastable vacuum decay in center-stabilized Yang-Mills theory at large $N$
journal, November 2014

QCD domain walls, Chern-Simons theories and holography
journal, September 2018

Do we live in the swampland?
journal, December 2018

Dihedral symmetry in $S U (N)$ Yang-Mills theory
journal, October 2019