Towards a quantum field theory description of nonlocal spacetime defects

TL;DR

This paper introduces a model for nonlocal spacetime defects in scalar field theory on causal sets, analyzing their effects on propagators and revealing defect-induced mass and wave-function renormalization.

Contribution

It proposes a novel ansatz for encoding nonlocal spacetime defects in Green's functions within causal set theory, enabling numerical analysis of defect effects.

Findings

Defects cause variation in propagation amplitudes depending on point types.

Average defect effects can be interpreted as mass and wave-function renormalization.

The continuum limit approaches expected results as the number of points increases.

Abstract

We propose an ansatz for encoding the physics of nonlocal spacetime defects in the Green's functions for a scalar field theory defined on a causal set. This allows us to numerically study the effects of nonlocal spacetime defects on the discrete Feynman propagator of the theory defined on the causal set in 1+1 dimensions, and to compare to the defect-free limit. The latter approaches the expected continuum result, on average, when the number of points becomes large. When defects are present, two points with the same invariant spacetime interval can have different propagation amplitudes, depending on whether the propagation is between two ordinary spacetime points, two defects, or a defect and an ordinary point. We show that a coarse-grained description that is only sensitive to the average effect of the defects can be interpreted as a defect-induced mass and wave-function renormalization of the scalar theory.