Consistency of $\chi$SB in chiral Yang-Mills theory with adiabatic continuity

TL;DR

This paper demonstrates that the pattern of chiral symmetry breaking in a specific chiral Yang-Mills model remains consistent when transitioning from small to large compactification radius, supporting the concept of adiabatic continuity.

Contribution

It provides a nonperturbative analysis of chiral symmetry breaking in a chiral Yang-Mills theory using adiabatic continuity and center-symmetric deformations.

Findings

Nonperturbative instanton-monopole effects induce chiral condensates.

Chiral symmetry breaking pattern is consistent across different coupling regimes.

Gauge symmetry is spontaneously broken to its maximal Abelian subgroup.

Abstract

We study the pattern of chiral symmetry breaking ($\chi$SB) in the $\psi\chi\eta$ model (with the chiral fermion sector containing $ \psi^{\{ij\}}$, $\chi_{[ij]}$, and $\eta_{i}^{A}$, see [1]) on $\mathbb{R}^3 \times S^{1}_{L}$ and derive implications to $\mathbb{R}^4$ physics. Center-symmetric vacua are stabilized by a double-trace deformation. With the center symmetry maintained at small $L(S^1)\ll \Lambda^{-1}$, i.e. at weak coupling, no phase transitions are expected in passing to large $L(S^1)\gg \Lambda^{-1}$ (here $\Lambda$ is the dynamical Yang-Mills scale). Starting with the small $L$-limit, we find the leading-order nonperturbative corrections in the given theory. The instanton-monopole operators induce the adjoint chiral condensate $\langle \psi^{\{ij\}}\chi_{[jk]}\rangle \neq 0$ at weak coupling i.e. at $L(S^1)\ll \Lambda^{-1}$. Then adiabatic continuity tells us that $\langle \psi^{\{ij\}}\chi_{[jk]}\rangle \neq 0$ exists on $\mathbb{R}^4$, in full accord with the prediction [2]. Simultaneously with $\langle \psi^{\{ij\}}\chi_{[jk]}\rangle \sim \Lambda^3\delta^i_k$ the SU($N_c$) gauge symmetry is spontaneously broken at strong coupling down to its maximal Abelian subgroup.