Extending the theory of random surfaces

[摘要] The theory of embedded random surfaces, equivalent to two-dimensional quantumgravity coupled to matter, is reviewed, further developed and partly generalizedto four dimensions. It is shown that the action of the Liouville field theory that describesrandom surfaces contains terms that have not been noticed previously. Theseterms are used to explain the phase diagram of the Sine-Gordon model coupled togravity, in agreement with recent results from lattice computations. It is also demonstratedhow the methods of two- dimensional quantum gravity can be applied tofour-dimensional Euclidean gravity in the limit of infinite Weyl coupling. Criticalexponents are predicted and an analog of the "c = 1 barrier" of two-dimensionalgravity is derived.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Physics