Two topics in 2D quantum field theory

[摘要] Two topics in two-dimensional quantum field theory are presented. The firstis a classification of 2- and 3-field rational conformal field theories. Using the factthat the fusion algebra of a RCFT is specified in terms of integers that are relatedto modular transformation properties, we classify 2- and 3-field chiral RCFT's. Weshow that the only possibilities for the non-trivial fusion rule in the 2-field case areφ x φ = 1 or φ x φ = 1 + φ. Similar results are obtained for the 3-field case. A partialclassification of possible conformal dimensions and central charges for these theoriesis also obtained. The second topic is in two-dimensional quantum gravity. Explicitcomputation of the non-perturbative correlation functions of the (1, q) models ofKdV-gravity is presented. This computation includes contributions from high genusas well as correlation functions of descendant fields. A ghost number conservationlaw for these models is derived from purely algebraic considerations. A hint of furtherselection rules is found.

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

[关键词] Physics