Lifshitz metric with hyperscaling violation from NS5-Dp states in string theory
In our previous papers we have shown how Lifshitz-like space-time (space-time having a Lifshitz scaling along with a hyperscaling violation) can arise by taking near horizon limits of certain intersecting solutions (F-string with D$p$-branes and also with two D-branes) of string theory. In this paper we construct intersecting bound state solutions in the form of NS5-D$p$-branes (with $1\leq p \leq 6$) of type II string theories. These are 1/4 BPS and threshold bound states unlike the known NS5-D$p$ bound states which are 1/2 BPS and non-threshold. We show that the near horizon limits of these solutions also lead to Lifshitz-like space-time with the dynamical scaling exponent $z=0$ and the hyperscaling violation exponent $\theta=9-p$. The spatial dimension of the boundary theory is $d=7-p$. The dilatons in these theories are not constant in general (except for $p=5$) and therefore produce RG flows. So, we also consider the strong coupling phases of these theories and find that these phases also have similar Lifshitz-like structures, except for $p=2$, where it has an AdS$_3$ structure.