Ichiro Oda

Topological pregauge-pregeometry

Abstract The pregauge-pregeometric action, i.e. the fundamental matter action whose quantum fluctuations give rise to the Einstein-Hilbert and the Yang-Mills actions, is investigated from the point of view of the topological field theory. We show that the scalar pregauge-pregeometric action is a topological invariant for appropriate choices of the internal gauge group. This model realizes the picture that the gravitational and internal gauge theory at the low energy scale is induced as the quantum effects of the topological field theory at the Planck scale.

Towards BRST quantization of pregeometry and topological pregeometry

Abstract We investigate the Dirac bracket algebra of the scalar pregeometry including topological pregeometry with BRST formalism, as the first step to its quantization. We examine unitarity of the S-matrix, derive the precise expression for induced gravity, and discuss how the gravity is induced from the topological theory.

Topological four-dimensional Einstein gravity

Abstract A theory of topological gravity is presented on a euclidean four-manifold. The gauge conditions for topological symmetries are singled out in such a way that not only the curvature 2-form is self-dual but also the torsion 2-form is vanishing. Thus the moduli space that we are now concerned with is just that of all the solutions of the Einstein equations with self-dual curvature, or that of hyper-Kahler manifolds.

Charged dilatonic black hole and Hawking radiation in two dimensions

Abstract We consider Callan, Giddings, Harvey and Stromingers (CGHS) two dimensional dilatonic gravity with electromagnetic interactions. This model can also be solved classically. Among the solutions describing static black holes, there exist extremal solutions which have zero temperature. In the extremal solutions, the space-time metric is not singular. We also obtain the solutions describing charged matter (chiral fermions) collapsing into black holes. Through the collapsing, not only the future horizon but the past horizon also is shifted. The quantum corrections including chiral anomaly are also discussed. In a way similar to the CGHS model, the curvature singularity also appears, except in the extremal case, when the matter collapses. The screening effects due to the chiral anomaly have a tendency to cloak the singularity.

Topological four-dimensional gravity

We construct a model of topological gravity in four space-time dimensions. Topological symmetries are gauge-fixed in three kinds of conditions, which are (i) self-duality on curvature and vanishing torsion, (ii) self-duality on both curvature and torsion, and (iii) Einstein space. We use as dynamical variables independent vierbein and spin connection, and/or metric tensor. We present non-trivial observables whose correlation functions give gravitational counterparts of Donaldsons polynomial invariants. Many future problems which might be solved within the present framework are simply pointed out

Semi-classical approach to charged dilatonic black hole in two dimensions

Abstract We consider an exactly solvable semi-classical theory of two-dimensional dilatonic gravity with electromagnetic interactions. As was done in the paper by Russo, Susskind and Thorlacius, the term which changes the kinetic term is added to the action. 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. In a region of the parameter space, the essential behaviour of the theory is similar to that of Callan, Giddings, Harvey and Stromingers dilatonic black hole theory modified in the paper by Russo, Susskind and thorlacius and the singularity formed by the collapsing matter emerges naked. We find, however, another region of the parameter space where the singularity disappears in a finite proper time. Furthermore, in the region of the parameter space, there appears a discontinuity in the metric on the trajectory of the collapsing matter, which would be a signal of topology change.