Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions

Tatsuhiro Misumi, Takuya Kanazawa

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

We investigate QCD with adjoint Dirac fermions on ℝ3 × S1 with generic boundary conditions for fermions along S 1. By means of perturbation theory, semiclassical methods and a chiral effective model, we elucidate a rich phase structure in the space spanned by the S1 compactification scale L, twisted fermionic boundary condition φ and the fermion mass m. We found various phases with or without chiral and center symmetry breaking, separated by first- and second-order phase transitions, which in specific limits (φ = 0, φ = π, L → 0 and m → ∞) reproduce known results in the literature. In the center- symmetric phase at small L, we show that Ünsal's bion-induced confinement mechanism is at work but is substantially weakened at φ ≠ 0 by a linear potential between monopoles. Through an analytic and numerical study of the PNJL model, we show that the order parameters for center and chiral symmetries (i.e., Polyakov loop and chiral condensate) are strongly intertwined at φ ≠ 0. Due to this correlation, a deconfined phase can intervene between a weak-coupling center-symmetric phase at small L and a strong-coupling one at large L. Whether this happens or not depends on the ratio of the dynamical fermion mass to the energy scale of the Yang-Mills theory. Implication of this possibility for resurgence in gauge theories is briefly discussed. In an appendix, we study the index of the adjoint Dirac operator on ℝ3 × S1 with twisted boundary conditions, which is important for semiclassical analysis of monopoles.

Original languageEnglish
Article number181
JournalJournal of High Energy Physics
Volume2014
Issue number6
DOIs
Publication statusPublished - 2014

Fingerprint

quantum chromodynamics
fermions
boundary conditions
monopoles
Yang-Mills theory
condensates
gauge theory
broken symmetry
perturbation theory
operators
symmetry
energy

Keywords

  • Phase Diagram of QCD
  • Phenomenological Models
  • Spontaneous Symmetry Breaking

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions. / Misumi, Tatsuhiro; Kanazawa, Takuya.

In: Journal of High Energy Physics, Vol. 2014, No. 6, 181, 2014.

Research output: Contribution to journalArticle

Misumi, Tatsuhiro ; Kanazawa, Takuya. / Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions. In: Journal of High Energy Physics. 2014 ; Vol. 2014, No. 6.
@article{a86e12f2596847f69da195cbaa75c0bd,
title = "Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions",
abstract = "We investigate QCD with adjoint Dirac fermions on ℝ3 × S1 with generic boundary conditions for fermions along S 1. By means of perturbation theory, semiclassical methods and a chiral effective model, we elucidate a rich phase structure in the space spanned by the S1 compactification scale L, twisted fermionic boundary condition φ and the fermion mass m. We found various phases with or without chiral and center symmetry breaking, separated by first- and second-order phase transitions, which in specific limits (φ = 0, φ = π, L → 0 and m → ∞) reproduce known results in the literature. In the center- symmetric phase at small L, we show that {\"U}nsal's bion-induced confinement mechanism is at work but is substantially weakened at φ ≠ 0 by a linear potential between monopoles. Through an analytic and numerical study of the PNJL model, we show that the order parameters for center and chiral symmetries (i.e., Polyakov loop and chiral condensate) are strongly intertwined at φ ≠ 0. Due to this correlation, a deconfined phase can intervene between a weak-coupling center-symmetric phase at small L and a strong-coupling one at large L. Whether this happens or not depends on the ratio of the dynamical fermion mass to the energy scale of the Yang-Mills theory. Implication of this possibility for resurgence in gauge theories is briefly discussed. In an appendix, we study the index of the adjoint Dirac operator on ℝ3 × S1 with twisted boundary conditions, which is important for semiclassical analysis of monopoles.",
keywords = "Phase Diagram of QCD, Phenomenological Models, Spontaneous Symmetry Breaking",
author = "Tatsuhiro Misumi and Takuya Kanazawa",
year = "2014",
doi = "10.1007/JHEP06(2014)181",
language = "English",
volume = "2014",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",
number = "6",

}

TY - JOUR

T1 - Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions

AU - Misumi, Tatsuhiro

AU - Kanazawa, Takuya

PY - 2014

Y1 - 2014

N2 - We investigate QCD with adjoint Dirac fermions on ℝ3 × S1 with generic boundary conditions for fermions along S 1. By means of perturbation theory, semiclassical methods and a chiral effective model, we elucidate a rich phase structure in the space spanned by the S1 compactification scale L, twisted fermionic boundary condition φ and the fermion mass m. We found various phases with or without chiral and center symmetry breaking, separated by first- and second-order phase transitions, which in specific limits (φ = 0, φ = π, L → 0 and m → ∞) reproduce known results in the literature. In the center- symmetric phase at small L, we show that Ünsal's bion-induced confinement mechanism is at work but is substantially weakened at φ ≠ 0 by a linear potential between monopoles. Through an analytic and numerical study of the PNJL model, we show that the order parameters for center and chiral symmetries (i.e., Polyakov loop and chiral condensate) are strongly intertwined at φ ≠ 0. Due to this correlation, a deconfined phase can intervene between a weak-coupling center-symmetric phase at small L and a strong-coupling one at large L. Whether this happens or not depends on the ratio of the dynamical fermion mass to the energy scale of the Yang-Mills theory. Implication of this possibility for resurgence in gauge theories is briefly discussed. In an appendix, we study the index of the adjoint Dirac operator on ℝ3 × S1 with twisted boundary conditions, which is important for semiclassical analysis of monopoles.

AB - We investigate QCD with adjoint Dirac fermions on ℝ3 × S1 with generic boundary conditions for fermions along S 1. By means of perturbation theory, semiclassical methods and a chiral effective model, we elucidate a rich phase structure in the space spanned by the S1 compactification scale L, twisted fermionic boundary condition φ and the fermion mass m. We found various phases with or without chiral and center symmetry breaking, separated by first- and second-order phase transitions, which in specific limits (φ = 0, φ = π, L → 0 and m → ∞) reproduce known results in the literature. In the center- symmetric phase at small L, we show that Ünsal's bion-induced confinement mechanism is at work but is substantially weakened at φ ≠ 0 by a linear potential between monopoles. Through an analytic and numerical study of the PNJL model, we show that the order parameters for center and chiral symmetries (i.e., Polyakov loop and chiral condensate) are strongly intertwined at φ ≠ 0. Due to this correlation, a deconfined phase can intervene between a weak-coupling center-symmetric phase at small L and a strong-coupling one at large L. Whether this happens or not depends on the ratio of the dynamical fermion mass to the energy scale of the Yang-Mills theory. Implication of this possibility for resurgence in gauge theories is briefly discussed. In an appendix, we study the index of the adjoint Dirac operator on ℝ3 × S1 with twisted boundary conditions, which is important for semiclassical analysis of monopoles.

KW - Phase Diagram of QCD

KW - Phenomenological Models

KW - Spontaneous Symmetry Breaking

UR - http://www.scopus.com/inward/record.url?scp=84904283789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904283789&partnerID=8YFLogxK

U2 - 10.1007/JHEP06(2014)181

DO - 10.1007/JHEP06(2014)181

M3 - Article

VL - 2014

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 6

M1 - 181

ER -