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 setup allows to introduce a parameter which is related to the 't Hooft coupling of a suitable large $N$ limit, in which $N\to \mathrm{\infty }$ 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.