SU(N) Multi-Skyrmions at Finite Volume

TL;DR

This paper investigates multi-soliton solutions in the SU(N) Skyrme model at finite volume, using a geometric approach that incorporates large N limits and symmetry analysis.

Contribution

It introduces a geometric method to analyze finite-volume effects in SU(N) Skyrmions without symmetry breaking, linking a parameter to the 't Hooft coupling in large N limits.

Findings

Parameter related to 't Hooft coupling affects symmetry properties.

Explicit finite-volume effects can be analyzed without breaking symmetries.

Large N limit with zero curvature background is studied.

Abstract

We study multi-soliton solutions of the four-dimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of $S^{2}$ into $CP^{N-1}$ and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric setup allows to introduce a parameter which is related to the 't Hooft coupling of a suitable large $N$ limit, in which $N\rightarrow\infty$ and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it.