The effective action for wormholes

Abstract

There is a strong similarity between space-time wormholes and the multiply connected topology that occurs in one- and two-dimensional quantum field theories, like Feynman diagrams and string theory. Integrating out such topological fluctuations gives rise to a quantum field theory on a topologically trivial manifold with effective interactions whose couplings are given by a-parameters. It is shown that these α-parameters are the moments of a single quantum field α on the superspace of the original theory. In the one-dimensional case, this superspace is space-time, but in higher-dimensional field theories, it will be infinite dimensional. However, the superspace for the string contains space-time as a mini-superspace. The single α-field on superspace can be dimensionally reduced to an infinite tower of fields on space-time. If the tachyon is projected out, the lowest members of this tower are the dilaton, graviton and anti-symmetric tensor fields. In the case of space-time wormholes, the α-field is defined on the superspace of General Relativity. There is a discussion of the implications of this for the suggestion that wormholes uniquely fix the values of the physical constants.