Eur. Phys. J. C (2015) 75: 443
https://doi.org/10.1140/epjc/s10052-015-3647-7

Regular Article - Theoretical Physics

SU(N) multi-Skyrmions at finite volume

¹ Centro de Estudios Científicos (CECS), 1469, Casilla, Valdivia, Chile
² Dipartimento di Fisica “E.R. Caianiello”, Universitá di Salerno, Via Giovanni Paolo II, 84084, Fisciano, SA, Italy
³ Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Universitá di Napoli Federico II, Via Cinthia, 80126, Napoli, Italy

^* e-mail: fcanforat@gmail.com
^** e-mail: canfora@cecs.cl

Received: 29 May 2015
Accepted: 27 August 2015
Published online: 23 September 2015

Abstract

We study multi-soliton solutions of the four-dimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of into and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric set-up allows to introduce a parameter which is related to the ’t Hooft coupling of a suitable large N limit, in which and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it.