Lifshitz-like systems and AdS null deformations

TL;DR

This paper explores lightlike deformations of AdS spaces in string theory, leading to Lifshitz-like anisotropic systems with variable gauge couplings, and analyzes their correlation functions and nongeometric string constructions.

Contribution

It introduces new lightlike deformations of AdS backgrounds that model Lifshitz-like systems with variable dilaton profiles, including detailed correlation function calculations.

Findings

Lifshitz-like anisotropic systems described by lightlike dilaton deformations.

Explicit solutions with linear dilaton enabling correlation function analysis.

Identification of nongeometric string constructions related to these deformations.

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 $\Phi(x^+)$ 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. 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.