Holography beyond conformal invariance and AdS isometry?

TL;DR

This paper proposes a generalized holographic duality framework that extends beyond conformal invariance and AdS isometry, based on a relation between bulk and boundary operators, applicable to various geometries and spins.

Contribution

It introduces a new relation between functional determinants of bulk and boundary operators, broadening holographic duality beyond traditional conformal and AdS settings.

Findings

Validates the relation for operators of general spin-tensor structure.

Supports numerous tests of AdS/CFT through partition functions and anomalies.

Discusses potential for extending the method beyond one-loop calculations.

Abstract

We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem from the bulk spacetime. This relation holds for operators of general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, and it apparently underlies numerous $O(N^0)$ tests of AdS/CFT correspondence, based on direct calculation of the bulk and boundary partition functions, Casimir energies and conformal anomalies. The generalized holographic duality is discussed within the concept of the "double-trace" deformation of the boundary theory, which is responsible in the case of large $N$ CFT coupled to the tower of higher spin gauge fields for the renormalization group flow between infrared and ultraviolet fixed points. Potential extension of this method beyond one-loop order is also briefly discussed.