Space–time filling branes in non-critical (super) string theories

Abstract

We consider solutions of (super) gravities associated to non-critical (super) string theories in arbitrary space–time dimension D = p + 3 , that describe generically non-extremal black p-branes charged under NSNS or RR gauge fields, embedded in some non-critical vacuum. In the case of vacuum (uncharged) backgrounds, we solve completely the problem obtaining all the possible solutions, that consist of the ( p + 1 ) -dimensional Minkowski space–times a linear dilaton times an S 1 , and a three parameter family of solutions that includes ( p + 1 ) -dimensional Minkowski space–times the cigar, and its T-dual ( p + 1 ) -dimensional Minkowski space–times the trumpet. For NSNS charged solutions, we also solve in closed form the problem, obtaining several families of solutions, that include in particular the fundamental non-critical string solution embedded in the cigar vacuum, recently found in [A.R. Lugo, M.B. Sturla, Phys. Lett. B 637 (2006) 338, hep-th/0604202], a solution that we interpret as a fundamental non-critical string embedded in the linear dilaton vacuum, and a two-parameter family of regular curvature solutions asymptotic to AdS 1 , 2 × S 1 . In the case of RR charged D p-branes solutions, an ansatz allows us to find a non-conformal, constant curvature, asymptotically AdS 1 , p + 1 space, T-dual to AdS 1 , p + 2 , together with a two-parameter family of solutions that includes the non-conformal, AdS black hole like solution associated with the earlier space. The solutions obtained by T-duality are Einstein spaces consisting of a two-parameter family of conformal, constant dilaton solutions, that include, in particular, the AdS black hole of [S. Kuperstein, J. Sonnenschein, JHEP 0407 (2004) 049, hep-th/0403254]. We speculate about the possible applications of some of them in the framework of the gauge-gravity correspondence.