Baryons, Skyrmions and $θ$-periodicity anomaly in chiral and vector-like gauge theories

TL;DR

The paper investigates baryons, Skyrmions, and θ-periodicity anomalies across a range of chiral and vector-like SU($N$) gauge theories with mixed representations, centered on the CFL phase. By computing the low-energy coset topology and applying anomaly-matching and CCWZ methods, it shows that Skyrmions are absent in the chiral models but heavy baryons can be stable due to unbroken symmetries, whereas vector-like theories feature Skyrmions that map to baryons and exhibit nontrivial WZW terms. It then analyzes θ-periodicity anomalies, finding that complete CFL matches the anomaly without new EFT degrees of freedom, while partial CFL generally requires additional infrared dynamics on domain walls, often realized as Chern–Simons theories. The work highlights a rich interplay between topological solitons, domain-wall physics, and anomaly constraints, suggesting deeper mechanisms may govern heavy-baryon stability and the reliability of Skyrmion descriptions in low-energy EFTs.

Abstract

In this paper, we study the baryons and solitons of chiral and vector-like $SU(N)$ gauge theories with matter in mixed one and two-index representations. Focusing on the Color-flavor locked (CFL) phase, we compute the topology of the coset of their low-energy EFT. We find that in the chiral models under consideration, Skyrmions are always absent. We also show, however, that some of these models admit heavy baryons that are expected to be stable, because their decay into the lighter degrees of freedom of the EFT is forbidden by the unbroken symmetry group. This mismatch suggests that some deeper dynamical mechanism must be responsible with either the instability of the seemingly stable heavy baryons or the unreliability of the Skyrme model in the low-energy EFT. In the vector-like models all the expected baryons are mirrored by Skyrmions. Then we turn to the study of domain walls. We determine some aspects of their dynamics by matching the $θ$-periodicity anomaly. We find that, for complete CFL, the $θ$-periodicity anomaly is always matched without introducing new dynamical degrees of freedom in the low-energy EFT. If part of the color group is unbroken, new dynamical degrees of freedom must be added to the low-energy EFT in the domain-wall background with few exceptions.

Figures (2)

• Figure 1: Lattice of possible baryonic charges. The area in purple is the fundamental cell. The light baryons do not span the entire lattice.
• Figure 2: Examples of the braking of the torus $U(1)_{\psi A} \times U(1)_{\eta A}$.