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On the role of Area Metrics in AdS/CFT

Aranya Bhattacharya, Lavish Chawla, Mario Flory, Mateusz Kulig

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.

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.

Paper Structure

This paper contains 22 sections, 138 equations, 1 table.

Table of Contents

  1. Introduction
  2. Existence of dual EMT
  3. Holographic Dictionary
  4. Known result; $w_{\mu\rho\nu\lambda}$ turned off:
  5. New result; $h_{{\mu\nu}}$ turned off:
  6. Full area fluctuation:
  7. Equations of Motion
  8. Lagrangian formulation
  9. Introducing Lanczos potentials
  10. Discussion
  11. Existence of dual EMT
  12. Holographic dictionary for the boundary EMT
  13. Equations of motion
  14. Lagrangian formulation
  15. Role of tracelessness and the need for Lagrange multipliers
  16. ...and 7 more sections