Topological Sum Rules and Spectral Flows of Chiral and Gravitational Axion-like Interactions

TL;DR

This paper investigates the structure of anomaly-driven interactions in quantum field theory, revealing universal sum rules and spectral flow behaviors that distinguish conformal from non-conformal regimes, with implications for axion-like particles and topological materials.

Contribution

It extends the analysis of anomaly poles and sum rules in chiral and gravitational anomalies, highlighting their spectral flow and self-similarity, and clarifies their physical interpretation beyond local effective actions.

Findings

Universal sum rules regulate anomaly interactions across kinematic regimes.

Spectral densities exhibit self-similarity in both conformal and non-conformal limits.

Anomaly poles are true particle poles only in the conformal limit, describable by kinetically mixed pseudoscalars.

Abstract

We examine the structure of off-shell effective actions arising from chiral and gravitational anomalies, focusing on the $JJJ_A$ (axial-vector/vector/vector) and $J_A TT $ (axial-vector/stress-energy tensors) correlators, relevant in the analysis of anomaly-driven interactions in perturbation theory. Our approach relies on conformal field theory in momentum space, extended to chiral anomalies. The analysis centers on the presence of both particle poles and anomaly poles within these interactions, characterizing their behavior both in the conformal and non conformal limits. Through explicit computations, we show that universal sum rules in the longitudinal sector regulate these interactions for all kinematic conditions, extending previous analysis, and we discuss the resulting spectral flow, an area law of the absorptive part of the anomaly form factors as one moves away from or returns to the conformal point. These features are absent in the local effective action of anomaly interactions, commonly used in the description of axion-like particles. The spectral densities in both cases are shown to be self-similar. Our results further show that anomaly poles correspond to true particle poles only in the conformal limit, when the interaction describes a massless S-matrix process supported on a null-surface. Under these conditions, they can be effectively described by two kinetically mixed pseudoscalar fields propagating on the light-cone. These studies find application in polarized deeply inelastic scattering, axion-like dark matter and analogue systems such as topological materials.