Semi-classical string solutions for N=1 SYM

We study semi-classically the dynamics of string solitons in the Maldacena-Nunez background, dual in the infra-red to N = 1, d = 4 SYM. For closed string configurations rotating in the S-2 x R space wrapped by the stack of N D-branes we find a behaviour that indicates the decoupling of the stringy Kaluza-Klein modes with sufficiently large R-symmetry charge. We show that the spectrum of a pulsating string configuration in S-2 coincides with that of a N = 2 super-sine-Gordon model. Closed string configurations spinning in the transversal S-3 give a relation of the energy and the conserved angular momentum identical to that obtained for configurations spinning in the S-5 of the AdS(5) x S-5, dual to N = 4 SYM. In order to obtain non-trivial relations between the energy and the spin, we also consider conical-like configurations stretching along a radial variable in the unwrapped directions of the system of D-branes and simultaneously along the transversal direction. We find that in this precise case, these configurations are unstable-contrary to other backgrounds, where we show that they are stable. We point out that in the Poincare-like coordinates used for the Maldacena-Nunez background it seems that it is not possible to reproduce the well-known field theory relation between the energy and the angular momentum. We reach a similar conclusion for the Klebanov-Strassler background, by showing that the conical-like configurations are also unstable. (C) 2003 Elsevier B.V. All rights reserved.