Comments on string theory backgrounds with non-relativistic conformal symmetry

TL;DR

This paper examines gravity duals of non-relativistic conformal systems obtained via discrete light-cone quantization of relativistic CFTs, emphasizing the breakdown of naive AdS DLCQ and the viability of gravity descriptions in sectors with large light-cone momentum. It constructs explicit finite-temperature and finite-density backgrounds with asymptotic non-relativistic conformal symmetry, including AdS5 plane-wave and AdS7 plane-wave cases, as well as dipole theories, and analyzes their thermodynamics and phase structure. A key technical contribution is the development of two consistent non-linear Kaluza-Klein reductions to five dimensions that yield massive vector fields, enabling robust holographic realizations of z = 2 and z = 4 non-relativistic backgrounds. The work also provides a concrete DLCQ of the M5-brane theory, relating it to a conformal quantum mechanics on instanton moduli space, and clarifies how TsT transformations interact with these backgrounds, laying groundwork for holographic renormalization in Schrödinger-type geometries.

Abstract

We consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories. If the field theory has a gravity dual, then the conformal quantum mechanical theory can have a gravity dual description in a suitable finite temperature and finite density regime. Using this we compute the thermodynamic properties of the system. We give an explicit example where we display both the conformal quantum mechanical theory as well as the gravity dual. We also discuss the string theory embedding of certain backgrounds with non-relativistic conformal symmetry that were recently discussed. Using this, we construct finite temperature and finite density solutions, with asymptotic non-relativistic conformal symmetry. In addition, we derive consistent Kaluza-Klein truncations of type IIB supergravity to a five dimensional theory with massive vector fields.