Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories

Abstract

We carry out a gauge invariant analysis of certain perturbations of D-2-branes solutions of low energy string theories. We get generically a system of second order coupled differential equations, and show that only in very particular cases it is possible to reduce it to just one differential equation. Later, we apply it to a multi-parameter, generically singular family of constant dilaton solutions of non-critical string theories in D dimensions, a generalization of that recently found in arXiv:0709.0471 [hep-th]. According to arguments coming from the holographic gauge theory-gravity correspondence, and at least in some region of the parameters space, we obtain glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special emphasis in the scalar metric perturbations not considered previously in the literature in the non critical setup. We compare our numerical results to those studied previously and to lattice results, finding qualitative and in some cases, tuning properly the parameters, quantitative agreement. These results seem to show some kind of universality of the models, as well as an irrelevance of the singular character of the solutions. We also develop the analysis for the T-dual, non trivial dilaton family of solutions, showing perfect agreement between them.