Lifshitz-like systems and AdS null deformations

Abstract

Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations of $Ad{S}_5\times X^5$ 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 $Ad{S}_4\times X^7$ in M-theory.

Latex, 20pgs, 1 eps fig; v2. references added; v3. minor clarifications added, to appear in PRD

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• Lifshitz/Schrödinger D-p-branes and dynamical exponents
• From D3-Branes to Lifshitz Space-Times
• Lifshitz Singularities
• Intersecting D-branes and Lifshitz-like space-time
• AdS null deformations with inhomogeneities
• From AdS to Schrödinger/Lifshitz dual space-times without or with hyperscaling violation
• Interpolating solution from AdS${}_5$ to hyperscaling violating Lifshitz space-time
• On a lightlike limit of entanglement
• On hvLif-like solutions in gauged Supergravity
• Beyond AdS Space-times, New Holographic Correspondences and Applications
• Schrödinger Spacetimes with Screen and Reduced Entanglement