On Yang-Mills Theories with Chiral Matter at Strong Coupling

TL;DR

This work addresses the challenging non-perturbative dynamics of Yang–Mills theories with chiral matter by formulating $Z_K$ orbifold chiral quivers on $R_3\times S_1$ and stabilizing the center symmetry with double-trace deformations $P[U_J]$, enabling analytic control at small $r(S_1)$. The authors show that monopole operators vanish in these chiral theories due to averaging over global angles, while magnetic bions generate a mass gap for dual photons and flux-ring operators saturate chiral condensates, yielding a pattern of discrete chiral symmetry breaking and linear confinement. They establish volume independence at $N=\infty$ via EK reduction, linking the dynamics on $R_4$ to a deformed reduced theory on $R_{4-d}\times T_d$ in the neutral sector, and discuss refined Abelian large-$N$ limits that reveal a transition from Abelian to non-Abelian confinement. The framework provides a controllable, semiclassical handle on strongly coupled chiral gauge theories and suggests new avenues for studying $R_4$ physics through reduced models, with potential implications for phenomenology and lattice formulations. Overall, the paper advances analytical tools to explore chiral gauge dynamics at strong coupling and proposes a bridge between small-volume semiclassical results and four-dimensional confinement phenomena.

Abstract

Strong coupling dynamics of Yang--Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of chiral, non-supersymmetric gauge theories, in particular, chiral quiver theories on $S_1 \times R_3 $. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect small-$r(S_1)$ to large-$r(S_1)$ physics ($R_4$ is the limiting case) where the double-trace deformations are switched off. In particular, occurrence of the mass gap in the gauge sector and linear confinement due to bions are analytically demonstrated. We find the pattern of the chiral symmetry realization which depends on the structure of the ring operators, a novel class of topological excitations. The deformed chiral theory, unlike the undeformed one, satisfies volume independence down to arbitrarily small volumes (a working Eguchi--Kawai reduction) in the large $N$ limit. This equivalence, may open new perspectives on strong coupling chiral gauge theories on $R_4$.

Figures (4)

• Figure 1: Orbifold gauge theories with odd number of nodes. Nodes represents SU$(N)$ gauge group factors, and arrows are Weyl fermions. The $K=1$ is ${\mathcal{N}}=1$ SYM theory and is vector-like. $K\geq 3$ are chiral since no gauge invariant mass term can be added to the Lagrangian.
• Figure 2: Internal chiral anomaly which must cancel after one sums over all fermion species in the triangle loop.
• Figure 3: The SU$(\infty)$ deformed chiral theory, unlike the original chiral theory which is expected to possess a center symmetry changing transition at $L_{\rm c} \sim \Lambda^{-1}$, satisfies full volume independence down to arbitrarily small volumes. The figure is adapted from Ref. Unsal:2008ch.
• Figure 4: Cartoon of the spectral properties of the lightest glueball as a function of $LN \Lambda$. At small $LN \Lambda$, a semi-classical analysis is possible and reliable. In this regime, Abelian confinement is operative. As $N\rightarrow \infty$, this window shrinks to zero in $r(S_1)$ and volume independence (and non-Abelian confinement) takes over at any finite $r(S_1)$.