Conformal anomaly for 2d and 4d dilaton coupled spinors

TL;DR

This paper calculates the conformal anomaly for 2d and 4d dilaton-coupled spinors, deriving effective actions and applying results to black hole physics and quantum gravity models.

Contribution

It introduces a classical transformation method to compute dilaton-dependent anomalies in 2d and 4d spinor theories, simplifying previous approaches.

Findings

Reproduces the anomaly term in the solvable RST model.

Derives dilaton-dependent chiral anomaly in 4d.

Shows quantum-corrected black hole solutions with multiple horizons.

Abstract

We study quantum dilaton coupled spinors in two and four dimensions. Making classical transformation of metric, dilaton coupled spinor theory is transformed to minimal spinor theory with another metric and in case of 4d spinor also in the background of the non-trivial vector field. This gives the possibility to calculate 2d and 4d dilaton dependent conformal (or Weyl) anomaly in easy way. Anomaly induced effective action for such spinors is derived. In case of 2d, the effective action reproduces, without any extra terms, the term added by hands in the quantum correction for RST model, which is exactly solvable. For 4d spinor the chiral anomaly which depends explicitly from dilaton is also found. As some application we discuss SUSY Black Holes in dilatonic supergravity with WZ type matter and Hawking radiation in the same theory. As another application we investigate spherically reduced Einstein gravity with 2d dilaton coupled fermion anomaly induced effective action and show the existence of quantum corrected Schwarszchild-de Sitter (SdS) (Nariai) BH with multiple horizon.