AdS/CFT Equivalence Transformation

TL;DR

This paper demonstrates a nonlinear holographic transformation linking conformal field theories in Minkowski space to brane actions in AdS space, revealing new insights into the AdS/CFT correspondence and conformal symmetry realization.

Contribution

It introduces an invertible change of variables that maps Minkowski space CFTs with broken conformal symmetry to brane actions in AdS, providing a new perspective on holography.

Findings

Establishes a nonlinear transformation between Minkowski CFTs and AdS brane actions.

Shows the conformal group realization can be nonlinear and field-dependent.

Discusses implications for quantum effective actions in AdS/CFT context.

Abstract

We show that any conformal field theory in d-dimensional Minkowski space, in a phase with spontaneously broken conformal symmetry and with the dilaton among its fields, can be rewritten in terms of the static gauge (d-1)-brane on AdS_(d+1) by means of an invertible change of variables. This nonlinear holographic transformation maps the Minkowski space coordinates onto the brane worldvolume ones and the dilaton onto the transverse AdS brane coordinate. One of the consequences of the existence of this map is that any (d-1)-brane worldvolume action on AdS_(d+1)\times X^m (with X^m standing for the sphere S^m or more complicated curved manifold) admits an equivalent description in Minkowski space as a nonlinear and higher-derivative extension of some conventional conformal field theory action, with the conformal group being realized in a standard way. The holographic transformation explicitly relates the standard realization of the conformal group to its field-dependent nonlinear realization as the isometry group of the brane AdS_(d+1) background. Some possible implications of this transformation, in particular, for the study of the quantum effective action of N=4 super Yang-Mills theory in the context of AdS/CFT correspondence, are briefly discussed.