Multiflavor QCD* on R_3 x S_1: Studying Transition From Abelian to Non-Abelian Confinement

TL;DR

The paper investigates how confinement in center-stabilized multiflavor QCD$^*$ on $R_3\times S_1$ evolves from Abelian to non-Abelian as the circle radius changes. It constructs a semiclassical framework with a center-stabilizing double-trace deformation that preserves center symmetry and induces a Higgsing $SU(N)\to U(1)^{N-1}$, leading to a 3D NJL-like infrared dynamics governed by monopole- and bion-induced effects, which generate a mass gap and linear confinement. The authors show two confinement regimes, with and without continuous χSB, and argue that the χSB scale is parametrically tied to the Abelian–non-Abelian transition, scaling as $L_{\chi SB} \sim \Lambda^{-1}/N$, falling in the same order as the deconfinement of the Abelian regime for large $N$. They propose that confinement without χSB characterizes Abelian confinement, while χSB accompanies non-Abelian confinement, and they discuss large-$N$ implications and lattice-testable predictions.

Abstract

The center-stabilized multiflavor QCD* theories formulated on R_3 x S_1 exhibit both Abelian and non-Abelian confinement as a function of the S_1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S_1), we show occurence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r(S_1), the multiflavor theories possess a single phase transition associated with breaking of the continuous chiral symmetry. We conjecture that the scale of the χSB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.

Figures (1)

• Figure 1: The center-symmetric configuration of the eigenvalues of the Polyakov line for SU$(5)$.