We examine the structure of off-shell effective actions arising from chiral and gravitational anomalies, focusing on the $⟨JJ{J}_A⟩$ (vector/vector/axial-vector) and $⟨TT{J}_A⟩$ (stress-energy tensors/axial-vector) correlators, relevant in the analysis of anomaly-driven interactions in perturbation theory. Our approach employs both perturbative methods and techniques in conformal field theory within momentum space, extended to encompass 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 nonconformal limits. Through explicit computations, we show that universal sum rules in the longitudinal sector regulate these interactions for all kinematic conditions, extending previous analysis. 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 axionlike particles. 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, axionlike dark matter, and analog systems such as topological materials.

Close

PrevNext

Reuse & PermissionsView figure in article

• 
• 
• 
• 
• 
• 

• Anomalies
• Effective field theory
• Form factors
• Particle interactions
• Perturbation theory
• Quantum field theory
• Sum rules