Intersecting D-branes and Lifshitz-like space-time

Abstract

In a previous paper [P. Dey and S. Roy, J. High Energy Phys. 06 (2012) 129] we have shown how Lifshitz-like space-times (space-times having Lifshitz scaling with hyperscaling violation) arise from $1/4$ Bogomol'nyi-Prasad-Sommerfield, threshold $\mathrm{F}\ensuremath{-}\mathrm{D}p$--bound state solutions of type II string theories in the near horizon limit. In this paper we show that similar structures also arise from the near horizon limit of $1/4$ Bogomol'nyi-Prasad-Sommerfield, threshold-intersecting D-brane solutions of type II string theories. Some of these solutions are standard ($\mathrm{D}p\ensuremath{-}\mathrm{D}(p+4)$ for $p=0$, 2) and some are nonstandard ($\mathrm{D}p\ensuremath{-}\mathrm{D}(p+2)$ for $p=1$, 2, 3), including $\mathrm{D}2\ensuremath{-}\mathrm{D}{2}^{\ensuremath{'}}$, $\mathrm{D}3\ensuremath{-}\mathrm{D}{3}^{\ensuremath{'}}$, and $\mathrm{D}4\ensuremath{-}\mathrm{D}{4}^{\ensuremath{'}}$ solutions. The dilatons of these solutions, in general, run (except in D2-D4 and $\mathrm{D}3\ensuremath{-}\mathrm{D}{3}^{\ensuremath{'}}$ cases) and produce renormalization group flows. We discuss the phase structures of these solutions. D2-D4 and $\mathrm{D}3\ensuremath{-}\mathrm{D}{3}^{\ensuremath{'}}$ in the near horizon limit do not produce Lifshitz-like space-time but give ${\mathrm{AdS}}_{3}$ spaces.