$\theta$-dependence and center symmetry in Yang-Mills theories

Abstract

We investigate the relation between the realization of center symmetry and the dependence on the topological parameter $\theta$ in $SU(N)$ Yang-Mills theories, exploiting trace deformations as a tool to regulate center symmetry breaking in a theory with a small compactified direction. We consider, in particular, $SU(4)$ gauge theory, which admits two possible independent deformations, and study, as a first step, its phase diagram in the deformation plane for two values of the inverse compactified radius going up to $L^{-1}\sim 500$ MeV, comparing the predictions of the effective 1-loop potential of the Polyakov loop with lattice results. The $\theta$-dependence of the various phases is then addressed, up to the fourth order in $\theta$, by numerical simulations: results are found to coincide, within statistical errors, with those of the standard confined phase iff center symmetry is completely restored and independently of the particular way this happens, i.e. either by local suppression of the Polyakov loop traces or by long range disorder.

11 paqges, 18 figures

References in corpus (18)

• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Volume independence in large Nc QCD-like gauge theories
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Finite size phase transitions in QCD with adjoint fermions
• New Phases of SU(3) and SU(4) at Finite Temperature
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Phase Transitions, theta Behavior and Instantons in QCD and its Holographic Model
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Metastable vacuum decay and $\theta$ dependence in gauge theory. Deformed QCD as a toy model
• Oblique Confinement at $\theta \ne 0$ in weakly coupled gauge theories with deformations
• Long range order in gauge theories. Deformed QCD as a toy model
• On the effective Lagrangian of CP^(N-1) models in the large N limit

Cited by in corpus (4)

• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• The Large $N_c$ limit of QCD on the lattice
• Reconfinement, localization and thermal monopoles in $SU(3)$ trace-deformed Yang-Mills theory
• Topology of trace deformed Yang-Mills theory