The Triality of Conformal Extensions of Three Kinds of Special Relativity

TL;DR

This paper explores the conformal extensions of different types of special relativity within Minkowski, de Sitter, and anti-de Sitter spaces, revealing a triality that relates their conformal structures and the AdS/CFT correspondence.

Contribution

It introduces a unified framework for conformal extensions of special relativity across Minkowski, de Sitter, and anti-de Sitter spaces, highlighting a triality and its relation to AdS/CFT.

Findings

Establishment of conformal structures on Mink/dS/AdS spaces

Identification of a triality among these conformal extensions

Connection to the conjectured AdS/CFT correspondence

Abstract

The conformal extensions of three kinds of special relativity with ISO(1,3)/SO(1,4)/SO(2,3) invariance on Mink/dS/AdS space, respectively, are realized on an SO(2,4)/Z_2 invariant projective null cone [N] as the (projective) boundary of the 5-d AdS-space. The relations among the conformal Mink/dS/AdS spaces, the motions of light signals and the conformal field theories on them can be given. Thus, there should be a triality for these conformal issues and the conjectured AdS/CFT correspondence.