Constructing an Explicit AdS/CFT Correspondence with Cartan Geometry

TL;DR

This paper establishes an explicit AdS/CFT correspondence using Cartan geometry for the Lie group SO(4,2), connecting two gravitational theories with different symmetries without relying on supersymmetry or holography.

Contribution

It constructs a novel explicit AdS/CFT correspondence framework based on Cartan geometry and Lie algebra structures, involving dual gravitational theories with different symmetries.

Findings

Develops two gravitational theories with AdS and conformal symmetry.

Shows a natural correspondence between the theories based on Lie algebra structures.

Creates a framework independent of supersymmetry and holography.

Abstract

An explicit AdS/CFT correspondence is shown for the Lie group $SO(4,2)$. The Lie symmetry structures allow for the construction of two physical theories through the tools of Cartan geometry. One is a gravitational theory that has anti-de Sitter symmetry. The other is also a gravitational theory but is conformally symmetric and lives on 8-dimensional biconformal space. These "extra" four dimensions have the degrees of freedom used to construct a Yang-Mills theory. The two theories, based on AdS or conformal symmetry, have a natural correspondence in the context of their Lie algebras alone where neither SUSY, nor holography, is necessary.