Interactions of Non-Abelian Global Strings

TL;DR

This paper investigates the interactions of non-Abelian global strings, revealing how their internal orientations affect forces between them, and extends known results to include finite volume effects and stability considerations.

Contribution

It derives the interaction forces between non-Abelian global strings for arbitrary orientations, generalizing the Magnus force and analyzing stability and volume effects.

Findings

Maximum repulsive force occurs when string orientations are aligned.

No force exists when orientations are maximally misaligned.

Finite volume corrections modify the Abelian string interaction results.

Abstract

Non-Abelian global strings are expected to form during the chiral phase transition. They have orientational zero modes in the internal space, associated with the vector-like symmetry SU(N)_{L+R} broken in the presence of strings. The interaction among two parallel non-Abelian global strings is derived for general relative orientational zero modes, giving a non-Abelian generalization of the Magnus force. It is shown that when the orientations of the strings are the same, the repulsive force reaches the maximum, whereas when the relative orientation becomes the maximum, no force exists between the strings. For the Abelian case we find a finite volume correction to the known result. The marginal instability of the previously known Abelian eta' strings is discussed.