Self-gravitating baryonic tubes supported by $\pi$- and $\omega$-mesons and its flat limit

TL;DR

This paper constructs self-gravitating topological solitons in an $SU(N)$ Einstein non-linear sigma model with $$-vector mesons, analyzing their properties and flat-space limits for arbitrary flavor numbers.

Contribution

It introduces a method to construct baryonic tube solutions for any number of flavors in an $SU(N)$ Einstein non-linear sigma model coupled to $$-vector mesons, extending previous models.

Findings

Solutions are tube-like, free of singularities, with topological charge proportional to flavor number.

Total energy increases with flavor number, but binding energy decreases, indicating improved physical predictions.

Flat-space limit corresponds to an array of baryonic tubes within finite volume.

Abstract

In this paper, we construct self-gravitating topological solitons in the $SU(N)$ Einstein non-linear sigma model coupled to $\omega$-vector mesons in four space-time dimensions. These solutions represent tube-like configurations free of curvature singularities, carrying a non-vanishing topological charge that is identified as the baryon number. We show that by employing the maximal embedding Ansatz of $SU(2)$ into $SU(N)$ in the exponential representation, these tubes can be constructed for an arbitrary number of flavors, $N$, with the topological charge scaling proportionally to this number. The flat-space limit of the solutions, corresponding to an array of baryonic tubes within a finite volume, is analyzed in detail. Remarkably, while the total energy of the solitons at a finite volume is an increasing function of $N$, the binding energy decreases as the number of flavors increases. This analysis reaffirms that the inclusion of more than two flavors to the model systematically improves the physical predictions.