Nonexistence of Skyrmion–Skyrmion and Skyrmion–anti-Skyrmion static equilibria

Abstract

We consider classical static Skyrmion-anti-Skyrmion and Skyrmion-Skyrmion configurations, symmetric with respect to a reflection plane, or symmetric up to a G-parity transformation respectively. We show that the stress tensor component completely normal to the reflection plane, and hence its integral over the plane, is negative definite or positive definite respectively. Classical Skyrmions always repel classical Skyrmions and classical Skyrmions always attract classical anti-Skyrmions and thus no static equilibrium, whether stable or unstable, is possible in either case. No other symmetry assumption is made and so our results also apply to multi-Skyrmion configurations. Our results are consistent with existing analyses of Skyrmion forces at large separation, and with numerical results on Skymion-anti-Skyrmion configurations in the literature which admit a different reflection symmetry. They also hold for the massive Skyrme model. We also point out that reflection symmetric self-gravitating Skyrmions or black holes with Skyrmion hair cannot rest in symmetric equilibrium with self-gravitating anti-Skyrmions.

Topological or rotational non-Abelian gauge fields from Einstein-Skyrme holography

“…The Skyrmions in (3+1)-dimensional flat space-time have been discussed as descriptions of pions with their topological charge identified as a baryon number. Previous studies have investigated the Skyrme model coupled to gravity (Einstein-Skyrme model) in (3 + 1)-dimensional space-time and have shown the existence of solitons and black hole solutions with hair [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. The quadratic term in the chiral fields present in these articles often led authors to numerical solutions of the field equations instead of analytic solutions for at least some of the fields.…”

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

“…In fact, Eqs. (17) and (19) describes a bound state of 4-Baryons whose energy density is localized. In the next section will be show that indeed, the energy of the 4-Baryon state is different from the one of the four Skyrmions on the SU (2) ansatz.…”

“…The Skyrme model has been deeply analyzed not only by its emergence in low energy QCD but also due to its relevance in General Relativity. For instance, black holes with a non-trivial Skyrme hair were found using numerical tools in [13][14][15] providing the first genuine counterexample to the well-known "no-hair" conjecture; unlike other supposedly "hairy" black holes that were unstable at the end [16], see also [17][18][19][21][22][23][24]. Cosmological applications of the Skyrme model have also been considered [25,26].…”

A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography

“…The Skyrmions in (3+1)-dimensional flat spacetime have been discussed as descriptions of pions with their topological charge identified as a baryon number. Previous studies have investigated the Skyrme model coupled to gravity (Einstein-Skyrme model) in (3+1)-dimensional spacetime and have shown the existence of solitons and black hole solutions with hair [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. The quadratic term in the chiral fields present in these articles often led authors to numerical solutions of the field equations instead of analytic solutions for at least some of the fields.…”