1/N Effects in Non-Relativistic Gauge-Gravity Duality

TL;DR

The paper investigates how higher-curvature corrections in gravity affect non-relativistic gauge-gravity duals, proving that Schrödinger and Lifshitz metrics remain non-renormalized in form while the dynamical exponent z can be renormalized by quantum effects. It builds explicit Type IIB string theory realizations with non-integer z, using perturbative corrections to compute shifts in z (e.g., z = 2 + 2/(27N) + ... for a beta-DLCQ of Sp(N) gauge theory) and argues that the viscosity/entropy ratio η/s can mildly violate the KSS bound in these NRCFTs. The work also extends the discussion to Lifshitz geometries and analyzes higher-curvature corrections in 4D and 5D contexts, highlighting both the robustness of NR geometries and the limitations due to the lack of fully explicit finite-temperature solutions. Overall, it provides a framework for understanding renormalization of z in NR holography and sets the stage for quantitative tests of NR strong-coupling dynamics.

Abstract

We argue that higher-curvature terms in the gravitational Lagrangian lead, via non-relativistic gauge-gravity duality, to finite renormalization of the dynamical exponent of the dual conformal field theory. Our argument includes a proof of the non-renormalization of the Schrodinger and Lifshitz metrics beyond rescalings of their parameters, directly generalizing the AdS case. We use this effect to construct string-theory duals of non-relativistic critical systems with non-integer dynamical exponents, then use these duals to predict the viscosity/entropy ratios of these systems. The predicted values weakly violate the KSS bound.