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Baryons, skyrmions, and θ-periodicity anomaly in chiral and vectorlike gauge theories

Stefano Bolognesi*

Andrea Luzio†

Giacomo Santoni‡

  • Theoretical Particle Physics Laboratory, EPFL, 1015 Lausanne, Switzerland

  • *Contact author: stefano.bolognesi@unipi.it
  • †Contact author: andrea.luzio@epfl.ch
  • ‡Contact author: giacomo.santoni@alumni.sns.it
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Phys. Rev. D 113, 105005 – Published 11 May, 2026

DOI: https://doi.org/10.1103/brm8-v5cc

Abstract

In this paper, we study the baryons and solitons of chiral and vectorlike 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 effective field theory (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 vectorlike 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.

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Phys. Rev. D 113, 105005– Published 11 May, 2026
  • Received 9 February 2026
  • Accepted 24 March 2026
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