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

Quantum fields in a curved background space lead to an anomalous trace of the total energy momentum tensor which can become macroscopic near black hole horizons. In two dimensions, the resulting effective action is the non-local Polyakov action. This effective action can be written in a local form by introducing one effective scalar field whose properties may hold the key to a better understanding of quantum effects in the near horizon region. In the present work, we found a curious relationship between tree graphs of stress-energy tensors of this new scalar field, and one-loop graphs of stress-energy tensors in terms of the original quantum fields. In particular, when starting from fermions the new scalar may be interpreted as an "interpolating" field describing intermediate two-fermion states. Finally, we compare our results to the chiral anomaly situation known from the Schwinger model in the context of bosonization, and draw parallels.