On the role of Area Metrics in AdS/CFT

TL;DR

This paper investigates how area metrics, a generalized geometric concept, influence the AdS/CFT correspondence, deriving a holographic dictionary, bulk equations, and proposing a bulk Lagrangian framework.

Contribution

It introduces a novel approach using area metrics in AdS/CFT, deriving equations of motion and a holographic dictionary for area metric fluctuations.

Findings

Derived bulk equations of motion for area metric fluctuations.

Established a holographic dictionary relating boundary and bulk geometries.

Proposed a bulk Lagrangian model based on Lanczos-like potentials.

Abstract

We explore the potential role of area metrics, a generalised notion of geometry, in the AdS/CFT correspondence. Guided by the Ryu-Takayanagi formula and the first law of entanglement, we derive both a holographic dictionary as well as a bulk equation of motion for area metric fluctuations linearised around a four dimensional AdS background. Furthermore, we explore potential bulk Lagrangians that could give rise to the derived equation. It is shown that writing area metric fluctuations in terms of Lanczos like potentials gives rise to a particularly elegant bulk model.