Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions

Abstract

We investigate QCD with adjoint Dirac fermions on ${\mathbb{R}}^3\times S^1$ 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 $S^1$ compactification scale $L$, twisted fermionic boundary condition $\varphi$ 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 ($\varphi =0$, $\varphi =\pi$, $L\to 0$ and $m\to \infty$) reproduce known results in the literature. In the center-symmetric phase at small $L$, we show that Unsal's bion-induced confinement mechanism is at work but is substantially weakened at $\varphi \ne 0$ 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 $\varphi \ne 0$. 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 ${\mathbb{R}}^3\times S^1$ with twisted boundary conditions, which is important for semiclassical analysis of monopoles.

43 pages, 14 figures. v2: references added, Section 3.1 expanded. The version to appear in JHEP

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Cited by in corpus (13)

• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• QCD on a small circle
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition
• $\theta$-dependence and center symmetry in Yang-Mills theories
• Critical behavior of gauge theories and Coulomb gases in three and four dimensions
• Properties of size-dependent models having quasiperiodic boundary conditions
• The absence of IR renormalons in gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and what it means for resurgence
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• The thermal instanton determinant in compact form
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$