Axion‐Like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

• Published in: Advanced Physics Research Vol. 4; no. 7
• Main Authors: Corianò, Claudio, Cretì, Mario, Lionetti, Stefano, Melle, Dario, Tommasi, Riccardo
• Format: Journal Article
• Language: English
• Published: Wiley-VCH 01.07.2025
• Subjects: field theory; quantum anomalies; topological materials
• ISSN: 2751-1200; 2751-1200
• DOI: 10.1002/apxr.202400043

Fundamental aspects of chiral anomaly‐driven interactions in conformal field theory (CFT) in four spacetime dimensions are discussed. These interactions find application in very general contexts, from early universe plasma to topological condensed matter. The key shared characteristics of these interactions are outlined, specifically addressing the case of chiral anomalies, both for vector currents and gravitons. In the case of topological materials, the gravitational chiral anomaly is generated by thermal gradients via the (Tolman–Ehrenfest) Luttinger relation. In the CFT framework, a nonlocal effective action, derived through perturbation theory, indicates that the interaction is mediated by excitation in the form of an anomaly pole, which appears in the conformal limit of the vertex. To illustrate this, it is demonstrated how conformal Ward identities (CWIs) in momentum space allow to reconstruct the entire chiral anomaly interaction in its longitudinal and transverse sectors just by inclusion of a pole in the longitudinal sector. Both sectors are coupled in amplitudes with an intermediate chiral fermion or a bilinear Chern–Simons current with intermediate photons. In the presence of fermion mass corrections, the pole transforms into a cut, but the absorption amplitude in the axial‐vector channel satisfies mass‐independent sum rules related to the anomaly in any chiral interaction. The detection of an axion‐like/quasiparticle in these materials may rely on a combined investigation of these sum rules, along with the measurement of the angle of rotation of the plane of polarization of incident light when subjected to a chiral perturbation. This phenomenon serves as an analog of a similar one in ordinary axion physics, in the presence of an axion‐like condensate, which is rederived using axion electrodynamics. This review investigates the connection between chiral anomalies and their manifestation in topological materials, using both perturbative methods based on ordinary quantum field theory and conformal field theory (CFT). It emphasizes the role of CFT in momentum space for parity‐odd correlation functions, and their reconstruction by the inclusion of a single axion‐like interaction. Both the nonlocal and the local anomaly actions induced by the chiral anomaly vertex are discussed, together with the fundamental equations of the (local) axion electrodynamics action, and the propagation of a light beam in the presence of an axion condensate.