Stability of the pion string in a thermal and dense medium

TL;DR

This paper studies the stability of pion strings in thermal and dense environments, finding stability depends on the chiral transition order and is enhanced by density, with implications for their persistence after core decay.

Contribution

It provides a detailed analysis of pion string stability in thermal and dense media, highlighting the dependence on chiral transition order and extending understanding to physical quark mass cases.

Findings

Stable pion strings exist only if the chiral transition is second order.

Density extends the stable region for pion strings.

String core decay does not eliminate the effective winding at large distances.

Abstract

We investigate the stability of the pion string in a thermal bath and a dense medium. We find that stability is dependent on the order of the chiral transition. String core stability within the experimentally allowed regime is found only if the chiral transition is second order, and even there the stable region is small, i.e., the temperature below which the core is unstable is close to the critical temperature of the phase transition. We also find that the presence of a dense medium, in addition to the thermal bath, enhances the experimentally accessible region with stable strings. We also argue that once the string core decays, the "effective winding" of the string persists at large distances from the string core. Our analysis is done both in the chiral limit, which is mainly what has been explored in the literature up to now, and for the physical $h \ne 0$ case, where a conceptual framework is set up for addressing this regime and some simple estimates are done.