Program

This talk will be about matter and the path integral in causal sets. I will report on recent work about simulating the 2d orders coupled to simple Ising spins, and some ongoing work about the scaling thereof. I will then probably wander of into some ideas (new and old) about how spin systems can encode the causal information for a causal set, and how this might help us with the path integral.

Defining a decoherence functional for causal sets has been a persistent obstacle in the path to quantum gravity. In this talk I will present the first known examples of decoherence functionals for causal sets. These decoherence functionals are obtained from the Classical Sequential Growth (CSG) models by a process of "quantization". I will present a diagnostic test which can be used to verify whether a given CSG model can quantized consistently. Based on work with Sumati Surya (arXiv:2003.11311).

To properly show that the horizon entropy of a black hole is proportional to its area we need to know the microscopic dynamics of causal sets. However, in analogy with a gas, one may still anticipate that the entropy can be estimated by counting the number of certain 'horizon molecules' without a knowledge of their dynamics. In this talk I will discuss a proposal for a definition of 'horizon molecules', and briefly comment on the connection with horizon entropy. I will also highlight some interesting aspects of the background calculations that could be useful for extracting more spatial geometry from causal sets in the future.

Entanglement entropy is a rich topic with important applications in quantum gravity. Causal sets have a lot to offer entanglement entropy, most notably a fundamental and covariant cutoff. I will review the current status of scalar field entanglement entropy in causal set theory. I will summarize past and recent work and highlight some of the open questions that remain, as well my thoughts on strategies for addressing them. I will end with a discussion of future directions.

We summarize the construction of the probability measure for the Poisson process called sprinkling to generate causal sets from a given spacetime manifold.

We also investigate the local structure of diamonds in sprinkled causal sets, where a 'diamond' is the Alexandrov interval spanned by two points that are separated by two links. These diamonds play an essential role in a recently proposed discretization method for the Klein-Gordon equation on causal sets. For this discretization, we need to choose a 'preferred past' from the two link past for each causet event. We test six criteria to reduce this choice and show numerical results for the diamonds that are spanned between a causet event and its two link past as selected by the criteria.

This talk is based on joint work with C. J. Fewster, E. Hawkins, and K. Rejzner.

We show 3 explicit examples of the use of Rafael's entanglement entropy formulation - de Sitter spacetime in 2, 4 dimensions and Minkowski spacetime in 4 dimensions. Due to the radical non-locality of the causal set we get volume laws for entropy in each case. We find that it is possible to obtain an area law when the spectrum of the Pauli-Jordan operator is truncated appropriately. However, having tried several ways of implementing the truncation, we find that it is hard to converge on one prescription. The truncation means augmenting the kernel of the Pauli-Jordan operator and is also tied to the notion of equations on motion and to violations of causality at the level of the causal set. We hope to discuss these issues with the wider causal set community.

In this talk, I will focus on the presence of boundary terms in the continuum limit of the causal set action. I will present a way to extend this topic 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 some new results about how the information encoded in a causal set can be useful to define a kinematical gravitational entropy. I will recall 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.

In this talk, I will present a modified version of the chain action for causal sets and compare its accuracy to the Benincasa Dowker action for causal sets embeddable in two dimensional manifolds. I will also propose a discrete variational principle, and the results of manifoldlike causal sets will be compared to Kleitman-Rothschild causal sets.