Hi all,
Abstract: The formulation of a quantum theory of gravity has been one of the major challenges for theoretical physicists in the last century. In this framework, the Causal Set Theory (CST) approach saw recent and rapid progress with the discovery of a discrete equivalent for the Einstein-Hilbert action. In this talk, after a rapid introduction of the CST formalism, I will describe the derivation of the causal set action, illustrate its continuum limit and how it can extract geometric information from the causal set structure. I will then focus on the presence of boundary terms in the continuum limit of the action and extend the discussion to a general curved space time. I will show that the action of a causal diamond in a Riemann normal neighbor effectively localizes to the null-null joint.

I will then discuss how the information encoded in a causal set can be useful to define a kinematical gravitational entropy. I will first consider the Horizon Molecules proposal, then I will introduce the Spacetime Mutual Information concept. I will argue that the SMI follows an area law when evaluated on causal diamonds cut by causal horizons. This result is promising in the search for a quantity giving a kinematical, then dynamical, discrete entropy for causal horizons in CST.

Preprint: https://arxiv.org/abs/2007.13192