Analytic self-gravitating $4$-Baryons, traversable NUT-AdS wormholes, flat space-time multi-Skyrmions at finite volume and a novel transition in the $SU(3)$-Skyrme model

TL;DR

This paper presents the first analytic self-gravitating $SU(3)$-Skyrmions with higher Baryon charge, including traversable wormholes and finite-volume Skyrmions, revealing a novel transition driven by Baryon density.

Contribution

It introduces explicit analytic $SU(3)$-Skyrmion solutions with Baryon charge 4 in a Bianchi IX universe and explores their gravitational and topological properties, including wormholes and phase transitions.

Findings

Analytic $SU(3)$-Skyrmion solutions with Baryon charge 4 constructed.

Traversable NUT-AdS wormholes supported by $SU(3)$-sigma solitons found.

A new transition at finite Baryon density between embedded and non-embedded solutions.

Abstract

We construct the first analytic self-gravitating Skyrmions with higher Baryon charge in four dimensions for the $SU(3)$-Skyrme-Einstein-$\Lambda$ theory by combining the generalized hedgehog ansatz with the approach developed by Balachandran et al. to describe the first (numerical) example of a non-embedded solution. These are genuine $SU(3)$ analytic solutions instead of trivial embeddings of $SU(2)$ into $SU(3)$ and its geometry is that of a Bianchi IX Universe. The Skyrme ansatz is chosen in such a way that the Skyrme field equations are identically satisfied in the sector with Baryon charge 4. The field equations reduce to a dynamical system for the three Bianchi IX scale factors. Particular solutions are explicitly analyzed. Traversable wormholes with NUT-AdS asymptotics supported by a topologically non-trivial $SU(3)$-sigma soliton are also constructed. The self-gravitating solutions admit also a suitable flat limit giving rise to Skyrmions of charge 4 confined in a box of finite volume maintaining the integrability of the $SU(3)$ Skyrme field equations. This formalism discloses a novel transition at finite Baryon density arising from the competition between embedded and non-embedded solutions in which the non-embedded solutions prevail at high density while are suppressed at low densities.