Semi-classical string solutions for N=1 SYM

TL;DR

This paper investigates semi-classical string solutions in the Maldacena-Nunez background, revealing insights into the spectrum, stability, and energy-spin relations of various string configurations dual to N=1 SYM and related theories.

Contribution

It provides new semi-classical solutions and analyzes their stability and spectral properties in the Maldacena-Nunez background, extending understanding of gauge/string duality for N=1 SYM.

Findings

Decoupling of stringy Kaluza-Klein modes at large SO(3) quantum numbers.

Spectrum of pulsating strings matches N=2 super Sine-Gordon model.

Conical-like string configurations are unstable in this background.

Abstract

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 behavior that indicates the decoupling of the stringy Kaluza-Klein modes with sufficiently large SO(3) quantum numbers. 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.