A Non-Renormalization Theorem in Gapped Quantum Field Theory

TL;DR

This paper proves that in certain gapped 3D quantum field theories, the parity-odd parts of key two-point functions are exactly determined at one loop, simplifying previous results and clarifying quantum correction subtleties.

Contribution

It provides a new, simplified derivation of the Coleman-Hill theorem and establishes a non-renormalization result for parity-odd correlators in gapped 3D theories.

Findings

Parity-odd two-point functions are one-loop exact.

The gravitational Chern-Simons term does not receive quantum corrections.

Clarifies subtleties in the original Coleman-Hill theorem.

Abstract

We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does not receive quantum corrections