Fermion Pairing and the Scalar Boson of the 2D Conformal Anomaly

Understand

We analyze the phenomenon of fermion pairing into an effective boson associated with anomalies and the anomalous commutators of currents bilinear in the fermion fields.

• In two spacetime dimensions the chiral bosonization of the Schwinger model is determined by the axial current anomaly of massless Dirac fermions.
• A similar bosonized description applies to the 2D conformal trace anomaly of the fermion stress tensor.
• For both the chiral and conformal anomalies, correlation functions involving anomalous currents, $j^{\mu}_5$ or $T^{\mu\nu}$ of massless fermions exhibit a massless boson $1/k^2$ pole, and the associated spectral functions obey a UV finite sum rule, becoming $\delta$-functions in the massless limit.