AdS/NRCFT for the (super) Calogero model

TL;DR

We address the problem of realizing a gravity dual for the non-relativistic (and supersymmetric) Calogero model. The approach builds deformed $AdS$ geometries that respect Schrödinger symmetry and realize a center-of-mass / internal (hyperradius) separation, extendable to $N$-particle systems and to superspace. The findings show that bulk/boundary dynamics reproduce the Calogero Hamiltonian with a clear mapping between bulk parameters and Calogero data, including scaling dimensions $Δ_±$ and a hyperradius interpretation, with generalization to mass-heterogeneous cases. This provides a concrete holographic framework for non-relativistic quantum many-body dynamics and opens a route to study multi-particle and supersymmetric Calogero systems via gravity.

Abstract

We propose a correspondence between the non-relativistic quantum Calogero model in d spatial dimensions and classical gravity theory in a deformed AdS_{d+3} background for single particle and AdS_{Nd+3} for N-particles. Later we extend our construction to the superspace for a super Calogero model.