Lifshitz-like systems and AdS null deformations
K. Narayan
TL;DR
The paper addresses holographic realizations of Lifshitz-like fixed points by studying lightlike deformations of AdS5×X5 in Type IIB supergravity, sourced by a null or linear dilaton Φ(x^+). It demonstrates that Launched from x^+-noncompact setups, the bulk exhibits anisotropic Lifshitz scaling with $z=2$ in the $(x^-,x_i)$ directions and $z=∞$ in the $(x^+,x^-)$ directions, and computes explicit 2-point functions in the linear-dilaton case, revealing how the dilaton potential shapes spatial correlation structure. It also develops a nongeometric DLCQ construction by making x^+$ periodic up to S-duality, fixing the asymptotic string coupling and allowing a conventional KK reduction to Lifshitz spacetimes; analogous axion-driven solutions are discussed. The work extends these holographic insights to AdS4×X7 in M-theory and highlights potential connections to c=1 string-like Liouville walls and to RG flows between Lifshitz and Schrödinger-like regimes, offering a framework for exploring anisotropic nonrelativistic dynamics in strongly coupled gauge theories.
Abstract
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 $Φ(x^+)$ 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. Following this, we discuss a nongeometric string construction involving a compactification along the $x^+$-direction of this linear dilaton system. We also point out similar IIB axionic solutions. Similar bulk arguments for $x^+$-noncompact can be carried out for deformations of $AdS_4\times X^7$ in M-theory.