Holographic formulation of 3D metric gravity with finite boundaries

Understand

In this work we construct holographic boundary theories for linearized 3D gravity, for a general family of finite or quasi-local boundaries.

• These boundary theories are directly derived from the dynamics of 3D gravity by computing the effective action for a geometric boundary observable, which measures the geodesic length from a given boundary point to some centre in the bulk manifold.
• We identify the general form for these boundary theories and find that these are Liouville like with a coupling to the boundary Ricci scalar.
• This is illustrated with various examples, which each offer interesting insights into the structure of holographic boundary theories.