Quantum Anomalies and Parity-odd CFT Correlators for Chiral States of Matter

TL;DR

This paper explores how chiral currents affect parity-odd correlators in conformal field theories, revealing that these interactions are governed by anomalies and involve a protected, nonlocal axion-like interaction.

Contribution

It demonstrates that parity-odd CFT correlators influenced by chiral currents can be fully determined by their anomaly structure through conformal constraints in momentum space.

Findings

Parity-odd correlators are fixed by anomaly content.

A single nonlocal axion-like interaction suffices.

Interaction remains protected at finite temperature and density.

Abstract

Chiral currents influence the parity-odd sector of CFT correlators in momentum space, playing a crucial role in the evolution of the quark-gluon plasma in the early universe. We demonstrate that these parity-odd interactions, which couple quarks and gluons to gravitons, can be fully determined in terms of their anomaly content by solving the conformal constraints in momentum space. This process involves a single nonlocal, massless axion-like interaction in the longitudinal channel, which remains protected against thermal and finite density effects.