AdS/CFT without holography: A hidden dimension on the CFT side and implications for black-hole entropy

TL;DR

This paper introduces a non-holographic version of AdS/CFT where both gravity and field theory exist in the same dimension, leading to new insights into black-hole entropy and the information paradox.

Contribution

It presents a novel non-holographic formulation of AdS/CFT with a hidden dimension linked to the UV cutoff, altering black-hole entropy interpretations.

Findings

Black-hole entropy scales with volume in the new framework.

Bekenstein-Hawking entropy is the minimal black-hole entropy.

Provides a resolution to the black-hole information paradox.

Abstract

We propose a new non-holographic formulation of AdS/CFT correspondence, according to which quantum gravity on AdS and its dual non-gravitational field theory both live in the same number D of dimensions. The field theory, however, appears (D-1)-dimensional because the interactions do not propagate in one of the dimensions. The D-dimensional action for the field theory can be identified with the sum over (D-1)-dimensional actions with all possible values $\Lambda$ of the UV cutoff, so that the extra hidden dimension can be identified with $\Lambda$. Since there are no interactions in the extra dimension, most of the practical results of standard holographic AdS/CFT correspondence transcribe to non-holographic AdS/CFT without any changes. However, the implications on black-hole entropy change significantly. The maximal black-hole entropy now scales with volume, while the Bekenstein-Hawking entropy is interpreted as the minimal possible black-hole entropy. In this way, the non-holographic AdS/CFT correspondence offers a simple resolution of the black-hole information paradox, consistent with a recently proposed gravitational crystal.