Action for Causal Set Theory

Causal Set Theory(CST) is one of many approaches to quantum gravity that assumes that continuous spacetime is an emergent phenomenon rather than fundamental. In CST, Spacetime is defined through the set of collections of discrete spacetime points which are related only by causality (also known as causal sets). These sets are the fundamental structure of spacetime. These sets must, however, provide us with continuum spacetime under continuum approximation. The kinematics of this theory has been worked out. One of many ways to build the dynamics for CST is by searching for a causal set analog of scalar curvature action.

This presentation aims to compare two ways of calculating these causal set versions of Scalar Curvature Action. One method is given by Bennincasa-Dowker action which introduces a nonlocal retarted linear operator on a scalar field of a causal set. This operator under local approximation can provide us with scalar curvature which in turn can be used to find the action. The other method is given by Dr. Luca Bombelli and Dr. Benjamin Pilgrim in the paper" A Tale of two Action". Using the expectation value of the 3-length chain, one can find its relationship with scalar curvature in curved spacetime. This can be used to define Chain Action. I will discuss all the pros and cons of these two methods in the presentation.