Self-gravitating baryonic tubes supported by $π$- and $ω$-mesons and its flat limit

TL;DR

The paper constructs self-gravitating tube-like solitons in the $SU(N)$ Einstein non-linear sigma model coupled to $\omega$-vector mesons, using a maximal embedding of $SU(2)$ into $SU(N)$ to keep the problem tractable for arbitrary flavor number. The authors obtain analytic profiles for the soliton in a Weyl-Lewis-Papapetrou background, show that the topological (baryon) charge per unit length scales as $B/L_z = n\bar{N}$ with $\bar{N}=\frac{N(N^2-1)}{6}$, and derive a flat-space limit that corresponds to a finite-volume array of tubes where the binding energy decreases with increasing flavor number. The inclusion of $\omega$-mesons is shown to flatten the energy density in one transverse direction and to reduce the binding energy across all $N$, with stronger reductions as the number of flavors grows. These results extend previous two-flavor constructions, provide a gravity-enabled, multi-flavor generalization of baryonic tubes, and suggest that larger flavor content yields more realistic predictions for baryon binding in effective chiral theories.

Abstract

In this paper, we construct self-gravitating topological solitons in the $SU(N)$ Einstein non-linear sigma model coupled to $ω$-vector-mesons in $D=4$ space-time dimensions. These solutions represent tube-like configurations free of curvature singularities and possess a non-vanishing topological charge identified as the baryon number. We show that, using the maximal embedding Ansatz of $SU(2)$ into $SU(N)$ in the exponential representation, the tubes can be constructed for arbitrary values of the flavor number, $N$, with the topological charge being proportional to this number. The flat limit of this solution, which corresponds to an array of baryonic tubes in a finite volume, is analyzed in detail. Remarkably, although the energy of the solitons at a finite volume is an increasing function of $N$, the binding energy decreases as the number of flavors present in the theory increases, reaffirming that the inclusion of more than two flavors improves the predictions of the model.

Figures (3)

• Figure 1: Energy density of the baryonic tube for different values of the flavor number. The presence of the $\omega$-mesons generates a flattening in one of the transverse directions. As the flavor number increases, the energy increases.
• Figure 2: Binding energy as a function of the baryon number of a system of baryons at a finite volume. The inclusion of the $\omega$-mesons reduces the binding energy for any value of the flavor number.
• Figure 3: Binding energy as a function of the flavor number for different values of $N$. As the number of flavors increases, the binding energy decreases.