Semi-Classical Approach to Black Holes in Two Dimensions

概要

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We review the recent development of quantum theories of two-dimensional dilatonic gravity based on the work of Oda and the author. We first consider the semi-classical theory of dilatonic gravity with electromagnetic interactions. The theory contains massless fermions as matter fields and there appear the quantum corrections including chiral anomaly. The screening effect due to the chiral anomaly has a tendency to cloak the singularity. We find a region of the parameter space where the singularity formed by the collapsing matter disappears in a finite proper time. We also analyze a supergravity theory coupled to a dilaton and superconformal matters. This theory is classically soluble and we find all the solutions appeared in Callan, Giddings, Harvey and Strominger's dilatonic gravity also satisfy the constraints and the equations of motion in this supersymmetric theory. When we quantize this theory by following the procedure of Distler, Hlousek and Kawai, the cosmological term is renormalized to vanish in the quantum action. As a result, any solution corresponding to classical black hole does not appear in the quantum theory.
理論物理学刊行会の論文
1994-01-31