SU(N) multi-Skyrmions at finite volume

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 S 2 into C P N - 1 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 N → ∞ 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.