Quantization in Ads and the Ads/CFT Correspondence

TL;DR

This paper explores alternative quantization methods in AdS space for scalar fields, proposing an improved AdS/CFT correspondence prescription that handles both regular and irregular modes more naturally, including various boundary conditions.

Contribution

It introduces a new quantization scheme in AdS that incorporates boundary terms, providing a unified and improved AdS/CFT correspondence framework for different mode types.

Findings

The new scheme naturally includes boundary terms.

It offers a unified treatment for regular and irregular modes.

The improved prescription handles various boundary conditions.

Abstract

The quantization of a scalar field in AdS leads to two kinds of normalizable modes, usually called regular and irregular modes. The regular one is easily taken into account in the standard prescription for the AdS/CFT correspondence. The irregular mode requires a modified prescription which we argue is not completely satisfactory. We discuss an alternative quantization in AdS which incorporates boundary terms in a natural way. Within this quantization scheme we present an improved prescription for the AdS/CFT correspondence which can be applied to both, regular and irregular modes. Boundary conditions other than Dirichlet are naturally treated in this new improved setting.