Quantum scalar field theories with fractional operators

TL;DR

This paper explores scalar quantum field theories with fractional non-local operators, analyzing their renormalization, unitarity, and finiteness properties in spacetimes with varying spectral dimensions.

Contribution

It introduces a class of fractional operator-based scalar theories, examining their renormalization and unitarity, and identifies conditions for finiteness and unitarity at one-loop and beyond.

Findings

Some theories are one-loop finite and unitary.

Certain models are ghost free or power-counting renormalizable but not both.

Theories can be finite and unitary at all orders under specific conditions.

Abstract

We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension. These theories are either ghost free or power-counting renormalizable but they cannot be both at the same time. However, some of them are one-loop unitary and finite, and possibly unitary and finite at all orders.