The first law of differential entropy and holographic complexity

Understand

We construct the CFT dual of the first law of spherical causal diamonds in three-dimensional AdS spacetime.

• A spherically symmetric causal diamond in AdS$_3$ is the domain of dependence of a spatial circular disk with vanishing extrinsic curvature.
• The bulk first law relates the variations of the area of the boundary of the disk, the spatial volume of the disk, the cosmological constant and the matter Hamiltonian.
• In this paper we specialize to first-order metric variations from pure AdS to the conical defect spacetime, and the bulk first law is derived following a coordinate based approach.