Path Integral Over Conformally Self-Dual Geometries

Details Path Integral Over Conformally Self-Dual Geometries Path Integral Over Conformally Self-Dual Geometries

1991-12-03

arxiv.org/abs/hep-th/9112005v2

Nucl.Phys. B390 (1993) 188-204

Physics

High Energy Physics

High Energy Physics - Theory

22 pages. Note added with predicted values for critical exponents and 4D analog of c=1 barrier

Scientific paper

10.1016/0550-3213(93)90391-2

The path integral of four dimensional quantum gravity is restricted to conformally self-dual metrics. It reduces to integrals over the conformal factor and over the moduli space of conformally self--dual metrics and can be studied with the methods of two dimensional quantum gravity in conformal gauge. The conformal anomaly induces an analog of the Liouville action. The proposal of David, Distler and Kawai is generalized to four dimensions. Critical exponents and the analog of the c=1 barrier of two dimensional gravity are derived. Connections with Weyl gravity and four dimensional topological gravity are suggested.

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