From Entanglement to Geometry: Area Metrics and New Bulk Degrees of Freedom in AdS/CFT

Holography has taught us that spacetime geometry is deeply 
tied to quantum entanglement. But if areas, rather than lengths, are the 
more fundamental observables in quantum gravity, should the bulk 
description still be based solely on an ordinary metric? In this talk, I 
will present a framework in which the AdS bulk is described by an area 
metric, a natural generalisation of geometry that assigns areas directly 
to two-dimensional surfaces. Using the Ryu–Takayanagi formula together 
with the first law of entanglement, I will show how such bulk 
fluctuations admit a holographic interpretation and how they modify the 
usual metric-based story in AdS/CFT. The analysis reveals that 
area-metric perturbations contain both the familiar length metric-like 
sector and genuinely new geometric degrees of freedom. These new modes 
can still couple to the boundary stress tensor and satisfy elegant bulk 
equations that resemble conformal spin-2 dynamics. I will also discuss 
how a formulation in terms of Lanczos-type potentials helps recover the 
Einstein limit while preserving the broader geometric structure. The 
overall picture suggests that holography may naturally accommodate a 
richer notion of bulk geometry than previously assumed, with possible 
implications for quantum gravity, emergence, and the encoding of 
non-classical bulk data.