Kerr-AdS black holes and non-relativistic conformal QM theories in diverse dimensions

TL;DR

This work develops a unified DLCQ framework for Kerr-AdS$_{d+3}$ black holes, producing backgrounds that are dual to non-relativistic conformal quantum mechanics in $d$ spatial dimensions on plane-wave boundaries. By performing the $a\to 1$ DLCQ limit across dimensions, the authors derive explicit gravity-side thermodynamics, including the Hamiltonian $H$, particle number $N$, temperature $T$, chemical potential $\mu$, and entropy $S$, and identify how these backgrounds embed in string/M-theory (e.g., AdS$_4\times S^7$, AdS$_6\times S^4$, AdS$_7\times S^4$). They analyze even/odd dimensional cases and a BTZ example, revealing a Hawking-Page-type transition at a critical temperature and outlining the role of internal manifolds’ isometries in prospective NRCQM duals. While explicit NRCQM field theories are not fully constructed, the gravity results provide concrete thermodynamic predictions and a roadmap for realizing NRCQM duals in diverse dimensions. The work thereby links higher-dimensional Kerr-AdS geometries, non-relativistic holography, and string/M-theory uplifts, advancing the study of strongly coupled NRCQM systems on plane-wave backgrounds.

Abstract

We study the discrete light cone quantization of Kerr-AdS_{d+3} black holes with a plane wave boundary. The resulting backgrounds are conjectured to be dual of non-relativist conformal quantum mechanical theories in d spatial dimensions at finite temperature and finite chemical potential. This includes the discrete light cone quantization of Kerr-AdS_4 and Kerr-AdS_6 black holes. These are conjectured to be dual of non-relativistic conformal quantum mechanical theories in one and three spatial dimensions, respectively, which are defined on plane wave backgrounds. We also consider the case of the BTZ black hole. We calculate thermodynamic properties of these systems by using the gravity dual models. We discuss the embedding of these backgrounds in string theory and M-theory. We give general formulas for the discrete light cone quantization of Kerr-AdS black holes in higher dimensions and their thermodynamic properties.