Semi-classical string solutions for [formula omitted] SYM

Abstract

We study semi-classically the dynamics of string solitons in the Maldacena–Nuñez background, dual in the infra-red to N=1 , d=4 SYM. For closed string configurations rotating in the S 2× 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× 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 Poincaré-like coordinates used for the Maldacena–Nuñez 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.