Skyrmions in Yang--Mills Theories with Massless Adjoint Quarks

TL;DR

This paper investigates the properties, stability, and microscopic interpretation of Skyrmions in SU(N_c) Yang--Mills theories with massless adjoint quarks, extending previous work to cases where N_f >= 3 and comparing with SO(N_c) theories.

Contribution

It derives the Wess--Zumino--Novikov--Witten term, analyzes Skyrmion statistics and fermion number, and compares different gauge theories with similar symmetry breaking patterns.

Findings

Skyrmion stability explained by abnormal statistics-fermion number relation

Derived the Wess--Zumino--Novikov--Witten term for the sigma model

Compared features of SU(N_c) and SO(N_c) gauge theories with adjoint fermions

Abstract

Dynamics of SU(N_c) Yang--Mills theories with N_f adjoint Weyl fermions is quite different from that of SU(N_c) gauge theories with fundamental quarks. The symmetry breaking pattern is SU(N_f) --> SO(N_f). The corresponding sigma model supports Skyrmions whose microscopic identification is not immediately clear. We address this issue as well as the issue of the Skyrmion stability. The case of N_f=2 had been considered previously. Here we discuss N_f >= 3. We discuss the coupling between the massless Goldstone bosons and massive composite fermions (with mass O(N_c^0)) from the standpoint of the low-energy chiral sigma model. We derive the Wess--Zumino--Novikov--Witten term and then determine Skyrmion statistics. We also determine their fermion number (mod 2) and observe an abnormal relation between the statistics and the fermion number. This explains the Skyrmion stability. In addition, we consider another microscopic theory -- SO(N_c) Yang--Mills with N_f Weyl fermions in the vectorial representation -- which has the same chiral symmetry breaking pattern and the same chiral Lagrangian. We discuss distinctive features of these two scenarios.