On the role of Area Metrics in AdS/CFT

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.