Comments on N=4 Superconformal Extension of the Calogero Model

TL;DR

This paper discusses the potential for an N=4 superconformal extension of the Calogero model to describe black hole horizons, focusing on constructing an SU(1,1|2) invariant model, especially for two particles.

Contribution

It explores the construction of an SU(1,1|2) invariant extension of the Calogero model and analyzes the two-particle case in detail, addressing challenges for larger systems.

Findings

Two-particle case analyzed in detail

Construction of SU(1,1|2) invariant extension proposed

Comments on complexities for n>2 systems

Abstract

Recently it was conjectured by Gibbons and Townsend that the large n limit of an N=4 superconformal extension of the n-particle Calogero model might provide a microscopic description of the extreme Reissner-Nordstrom black hole near the horizon. In this paper a possibility to construct an SU(1,1|2) invariant extension of the Calogero model is considered. We treat in detail the two-particle case and comment on some peculiarities intrinsic to n>2 generalizations.