Inhomogeneous pion condensed phase hosting topologically stable baryons

TL;DR

This paper explores an inhomogeneous pion condensate phase in chiral perturbation theory, revealing how spatial modulation of pion fields can host stable baryons characterized by topological charge, providing insights into baryon-pion interactions.

Contribution

It presents an analytic solution for inhomogeneous pion condensates with topological charge, linking pion modulation to baryon hosting in a novel way.

Findings

Analytic solution for inhomogeneous pion condensate in (3+1)D

Topological charge corresponds to baryon number in the condensate

System can host multiple baryons at fixed spatial positions

Abstract

We discuss the inhomogeneous pion condensed phase within the framework of chiral perturbation theory. We show how the general expression of the condensate can be obtained solving three coupled differential equations, expressing how the pion fields are modulated in space. Upon using some simplifying assumptions, we determine an analytic solution in (3+1)-dimensions. The obtained inhomogeneous condensate is characterized by a non-vanishing topological charge, which can be identified with the baryonic number. In this way, we obtain an inhomogeneous system of pions hosting an arbitrary number of baryons at fixed positions in space.