Analytic SU(N) Skyrmions at finite Baryon density

TL;DR

This paper constructs explicit analytic SU(N) Skyrmions at finite baryon density, revealing smooth layered structures with properties that can be calculated explicitly, and compares well with experimental and numerical results.

Contribution

It introduces a new class of analytic SU(N) Skyrmions at finite density that are not simple embeddings, providing explicit calculations of their properties and large N behavior.

Findings

Energy to baryon charge ratio computed for any N.

Skyrmions exhibit lasagna-like density profiles.

Analytical shear modulus estimates align with numerical studies.

Abstract

We construct analytic (3+1)-dimensional Skyrmions living at finite Baryon density in the SU(N) Skyrme model that are not trivial embeddings of SU(2) into SU(N). We used Euler angles decomposition for arbitrary N and the generalized hedgehog Ansatz at finite Baryon density. The Skyrmions of high topological charge that we find represent smooth Baryonic layers whose properties can be computed explicitly. In particular, we determine the energy to Baryon charge ratio for any N showing the smoothness of the large N limit. The closeness to the BPS bound of these configurations can also be analyzed. The energy density profiles of these finite density Skyrmions have \textit{lasagna-like} shape in agreement with recent experimental findings. The shear modulus can be precisely estimated as well and our analytical result is close to recent numerical studies in the literature.