Flow of Hagedorn singularities and phase transitions in large N gauge theories

Cherman, Aleksey; Kamata, Syo; Schäfer, Thomas; Ünsal, Mithat

doi:10.1103/PhysRevD.101.014012

Title: Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories

Abstract

We investigate the singularity structure of the (-1)^F graded partition function in QCD with n_f≥1 massive adjoint fermions in the large-N limit. Here, F is fermion number and N is the number of colors. The large N partition function is made reliably calculable by taking space to be a small three-sphere S³. Singularities in the graded partition function are related to phase transitions and to Hagedorn behavior in the (-1)^F-graded density of states. We study the flow of the singularities in the complex “inverse temperature” β plane as a function of the quark mass. This analysis is a generalization of the Lee-Yang-Fisher-type analysis for a theory which is always in the thermodynamic limit thanks to the large N limit. We identify two distinct mechanisms for the appearance of physical Hagedorn singularities and center-symmetry changing phase transitions at real positive β, inflow of singularities from the β=0 point, and collisions of complex conjugate pairs of singularities.

Authors:

Cherman, Aleksey; Kamata, Syo;

; Ünsal, Mithat

Publication Date:: Wed Jan 15 00:00:00 EST 2020

Research Org.:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1591703

Alternate Identifier(s):: OSTI ID: 1777083

Grant/Contract Number:: FG02-03ER41260

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Cherman, Aleksey, Kamata, Syo, Schäfer, Thomas, and Ünsal, Mithat. Flow of Hagedorn singularities and phase transitions in large N gauge theories.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.014012.

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                    Cherman, Aleksey, Kamata, Syo, Schäfer, Thomas, & Ünsal, Mithat. Flow of Hagedorn singularities and phase transitions in large N gauge theories.  United States.  https://doi.org/10.1103/PhysRevD.101.014012

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                    Cherman, Aleksey, Kamata, Syo, Schäfer, Thomas, and Ünsal, Mithat. Wed .  
"Flow of Hagedorn singularities and phase transitions in large N gauge theories".  United States.  https://doi.org/10.1103/PhysRevD.101.014012.

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@article{osti_1591703,

  title        = {Flow of Hagedorn singularities and phase transitions in large N gauge theories},

  author       = {Cherman, Aleksey and Kamata, Syo and Schäfer, Thomas and Ünsal, Mithat},

  abstractNote = {We investigate the singularity structure of the (-1)F graded partition function in QCD with nf≥1 massive adjoint fermions in the large-N limit. Here, F is fermion number and N is the number of colors. The large N partition function is made reliably calculable by taking space to be a small three-sphere S3. Singularities in the graded partition function are related to phase transitions and to Hagedorn behavior in the (-1)F-graded density of states. We study the flow of the singularities in the complex “inverse temperature” β plane as a function of the quark mass. This analysis is a generalization of the Lee-Yang-Fisher-type analysis for a theory which is always in the thermodynamic limit thanks to the large N limit. We identify two distinct mechanisms for the appearance of physical Hagedorn singularities and center-symmetry changing phase transitions at real positive β, inflow of singularities from the β=0 point, and collisions of complex conjugate pairs of singularities.},

  doi          = {10.1103/PhysRevD.101.014012},

  journal      = {Physical Review D},

  number       = 1,

  volume       = 101,

  place        = {United States},

  year         = {Wed Jan 15 00:00:00 EST 2020},

  month        = {Wed Jan 15 00:00:00 EST 2020}

}

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Title: Flow of Hagedorn singularities and phase transitions in large N gauge theories

Abstract

Citation Formats

Bose-Fermi cancellations without supersymmetry journal, May 2019

The 2-loop partition function of large N gauge theories with adjoint matter on S 3 journal, December 2009

Number of degrees of freedom, density of states and tachyons in string theory and CFT journal, July 1991

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

Nonperturbative volume reduction of large- N QCD with adjoint fermions journal, September 2009

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

Bose-Fermi degeneracies in large N adjoint QCD journal, July 2015

Large N limits as classical mechanics journal, April 1982

The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice journal, January 2010

Volume independence in large N c QCD-like gauge theories journal, June 2007

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve journal, November 2018

Phases of N = ∞ QCD-like gauge theories on S 3 × S 1 and nonperturbative orbifold-orientifold equivalences journal, July 2007

Volume Independence in the Large N Limit and an Emergent Fermionic Symmetry journal, September 2013

Weak-coupling analysis of the single-site large- N gauge theory coupled to adjoint fermions journal, June 2013

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

Casimir Energy of Confining Large N Gauge Theories journal, June 2015

Gauge Fields and Space-Time journal, October 2002

Modular invariance, finiteness, and misaligned supersymmetry: New constraints on the numbers of physical string states journal, November 1994

Exponential hadronic spectrum and quark liberation journal, October 1975

Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model journal, August 1952

QCD and instantons at finite temperature journal, January 1981

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

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories journal, January 2004

The Hagedorn spectrum and large N c QCD in 2 + 1 and 3 + 1 dimensions journal, August 2011

Behavior of lacunary series at the natural boundary journal, November 2009

String Theory, Misaligned Supersymmetry, and the Supertrace Constraints journal, June 1995

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

Wilson line in finite-temperature gauge theories journal, May 1982

Hagedorn Temperature of AdS 5 / CFT 4 via Integrability journal, February 2018

Mass anomalous dimension of adjoint QCD at large N from twisted volume reduction journal, August 2015

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

Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions journal, July 2013

Large- N reduction in QCD with two adjoint Dirac fermions journal, May 2012

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

First order deconfinement transition in large N Yang-Mills theory on a small S 3 journal, June 2005

Quantum Phase Transitions and New Scales in QCD-like Theories journal, May 2009

Realization of center symmetry in two adjoint flavor large-N Yang-Mills journal, August 2010

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

The Hagedorn transition, deconfinement and SYM theory journal, May 2000

QCD and the Hagedorn spectrum journal, June 2010

Finite volume phases of large- N gauge theories with massive adjoint fermions journal, November 2009

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

4 D − 2 D equivalence for large- N Yang-Mills theory journal, November 2015

Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter journal, June 2016

Title: Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories

Bose-Fermi cancellations without supersymmetry
journal, May 2019

The 2-loop partition function of large N gauge theories with adjoint matter on S ³
journal, December 2009

Number of degrees of freedom, density of states and tachyons in string theory and CFT
journal, July 1991

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

Nonperturbative volume reduction of large- $N$ QCD with adjoint fermions
journal, September 2009

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

Bose-Fermi degeneracies in large N adjoint QCD
journal, July 2015

Large $N$ limits as classical mechanics
journal, April 1982

The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice
journal, January 2010

Volume independence in large N _c QCD-like gauge theories
journal, June 2007

The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
journal, November 2018

Phases of $N = \infty$ QCD-like gauge theories on $S^{3} \times S^{1}$ and nonperturbative orbifold-orientifold equivalences
journal, July 2007

Volume Independence in the Large $N$ Limit and an Emergent Fermionic Symmetry
journal, September 2013

Weak-coupling analysis of the single-site large- N gauge theory coupled to adjoint fermions
journal, June 2013

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

Casimir Energy of Confining Large $N$ Gauge Theories
journal, June 2015

Gauge Fields and Space-Time
journal, October 2002

Modular invariance, finiteness, and misaligned supersymmetry: New constraints on the numbers of physical string states
journal, November 1994

Exponential hadronic spectrum and quark liberation
journal, October 1975

Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
journal, August 1952

QCD and instantons at finite temperature
journal, January 1981

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

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories
journal, January 2004

The Hagedorn spectrum and large N c QCD in 2 + 1 and 3 + 1 dimensions
journal, August 2011

Behavior of lacunary series at the natural boundary
journal, November 2009

String Theory, Misaligned Supersymmetry, and the Supertrace Constraints
journal, June 1995

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

Wilson line in finite-temperature gauge theories
journal, May 1982

Hagedorn Temperature of ${AdS}_{5} / {CFT}_{4}$ via Integrability
journal, February 2018

Mass anomalous dimension of adjoint QCD at large N from twisted volume reduction
journal, August 2015

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

Twisted space-time reduced model of large $N$ QCD with two adjoint Wilson fermions
journal, July 2013

Large- $N$ reduction in QCD with two adjoint Dirac fermions
journal, May 2012

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

First order deconfinement transition in large $N$ Yang-Mills theory on a small $S^{3}$
journal, June 2005

Quantum Phase Transitions and New Scales in QCD-like Theories
journal, May 2009

Realization of center symmetry in two adjoint flavor large-N Yang-Mills
journal, August 2010

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

The Hagedorn transition, deconfinement and SYM theory
journal, May 2000

QCD and the Hagedorn spectrum
journal, June 2010

Finite volume phases of large- N gauge theories with massive adjoint fermions
journal, November 2009

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

$4 D − 2 D$ equivalence for large- $N$ Yang-Mills theory
journal, November 2015

Modularity and 4D-2D spectral equivalences for large-N gauge theories with adjoint matter
journal, June 2016