Holographic Renormalisation for the Spin-3 Theory and the (A)dS3/CFT2 correspondence

TL;DR

This paper computes two-point functions for spin-3 fields in (A)dS3 using holographic renormalisation, confirming conformal invariance in AdS and analyzing consistency with asymptotic symmetries and central charges.

Contribution

It provides the first detailed holographic renormalisation analysis for spin-3 theories in (A)dS3 and explores their conformal and asymptotic symmetry properties.

Findings

Results are consistent with 2D conformal invariance in AdS3.

Similar results are obtained for dS3, supporting the dS/CFT correspondence.

The findings suggest incompatibility with previously proposed imaginary central charges in dS3.

Abstract

We compute the two-point correlation functions for the spin-3 theory in three dimensional (Anti-) de Sitter spacetimes by using holographic renormalisation. For the AdS case, we find results consistent with the general requirements of two-dimensional conformal invariance. In the de Sitter case, we find similar results. We discuss consistency requirements on the three point functions TWW for our results to be compatible with the asymptotic symmetry algebra for AdS case and with the de-Sitter central charge found in hep-th/0106113 by analyzing the stress-tensor. We also discuss why it is very likely that our results are not compatible with the imaginary central charge previously found for higher-spin theories in dS(3).