Lifshitz-like systems and AdS null deformations

Understand

Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations of $AdS_5\times X^5$ in Type IIB string theory sourced by a lightlike dilaton $\Phi(x^+)$ dual to the N=4 super Yang-Mills theory with a lightlike varying gauge coupling.

• We argue that in the case where the $x^+$-direction is noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems with a potential in the $x^+$-direction generated by the lightlike dilaton.
• We then describe solutions of this sort with a linear dilaton.
• This enables a detailed calculation of 2-point correlation functions of operators dual to bulk scalars and helps illustrate the spatial structure of these theories.