Continuous matter fields in Regge calculus

TL;DR

The paper demonstrates that continuous matter fields are ill-defined in 4D Regge calculus due to singular curvature distributions, suggesting discretising matter fields as a potential solution.

Contribution

It identifies the ill-defined nature of continuous matter fields in 4D Regge calculus and proposes discretisation as a possible resolution.

Findings

Effective action has infinite terms unremovable by UV renormalisation.

Singular curvature distribution causes ill-defined matter fields.

Discretisation of matter fields may resolve the issue.

Abstract

We find that the continuous matter fields are ill-defined in Regge calculus in the physical 4D theory since the corresponding effective action has infinite terms unremovable by the UV renormalisation procedure. These terms are connected with the singular nature of the curvature distribution in Regge calculus, namely, with the presence in d>2 dimensions of the (d-3)-dimensional simplices where the (d-2)-dimensional ones carrying different conical singularities are meeting. Possible resolution of this difficulty is discretisation of matter fields in Regge background.