Inhomogeneous pion condensed phase hosting topologically stable baryons

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.

Comments: 8 pages, 4 figures, contribution to the proceedings of "A Virtual Tribute to Quark Confinement and the Hadron Spectrum" August 2nd-6th 2021 (online)