Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density

TL;DR

This paper constructs explicit analytic solutions in the SU(N)-Skyrme model to describe different nuclear pasta phases at finite density, revealing how phase preferences depend on density and flavor number, and analyzing their energetic and structural properties.

Contribution

It provides the first explicit analytic solutions for nuclear pasta phases in the SU(N)-Skyrme model, including their energy and phase behavior at various densities and flavor numbers.

Findings

Nuclear spaghetti and lasagna phases are explicitly modeled.

Phase preference depends on density and flavor number.

Analytic solutions remain integrable with subleading corrections.

Abstract

We construct explicit analytic solutions of the $SU(N)$-Skyrme model (for generic $N$) suitable to describe different phases of nuclear pasta at finite volume in $(3+1)$ dimensions. The first type are crystals of Baryonic tubes (nuclear spaghetti) while the second type are smooth Baryonic layers (nuclear lasagna). Both, the ansatz for the spaghetti and the ansatz for the lasagna phases, reduce the complete set of Skyrme field equations to just one integrable equation for the profile within sectors of arbitrary high topological charge. We compute explicitly the total energy of both configurations in terms of the flavor number, the density and the Baryonic charge. Remarkably, our analytic results allow to compare explicitly the physical properties of nuclear spaghetti and lasagna phases. Our construction shows explicitly that, at lower densities, configurations with $N=2$ light flavors are favored while, at higher densities, configurations with $N=3$ are favored. Our construction also proves that in the high density regime (but still well within the range of validity of the Skyrme model) the lasagna configurations are favored while at low density the spaghetti configurations are favored. Moreover, the integrability property of the present configurations is not spoiled by the inclusion of the subleading corrections to the Skyrme model arising in the 't Hooft expansion. Finally, we briefly discuss the large $N$ limit of our configurations.