Some Exact Results in Chiral Gauge Theories

TL;DR

This paper investigates the non-perturbative dynamics of specific chiral SU(N) gauge theories, revealing symmetry breaking patterns and massless fermion spectra through anomaly matching and continuity with supersymmetric models.

Contribution

It provides new exact results on the spontaneous symmetry breaking and massless fermion content in chiral gauge theories with odd and even N, differing from previous tumbling models.

Findings

For odd N, global SU(N-4) breaks to Sp(N-5) with N-5 massless fermions.

For even N, the unbroken symmetry is Sp(N-4) with no massless fermions.

Results align with anomaly matching and continuity with supersymmetric theories.

Abstract

We analyze dynamics of chiral gauge theories based on the $SU(N)$ gauge group with one anti-symmetric tensor $A$ and $(N-4)$ anti-fundamentals $F_{i}$ when $N$ is odd. Based on the continuity to the supersymmetric gauge theories with anomaly-mediated supersymmetry breaking, we claim that the global $SU(N-4)$ symmetry is spontaneously broken to $Sp(N-5)$. There are $N-5$ massless fermions as a fundamental representation of $Sp(N-5)$, and another massless fermion, together saturating the anomaly matching conditions. When $N$ is even, the unbroken flavor symmetry is $Sp(N-4)$ while there are no massless fermions. Our result is different from the dynamics suggested by tumbling where the full $SU(N-4)$ symmetry is unbroken, but the tumbling picture can be modified via the addition of a second condensate to produce the symmetry breaking pattern predicted from our method.