Monodromy Representations of the Braid Group

Abstract

Chiral conformal blocks in a rational conformal field theory are a far going extension of Gauss hypergeometric functions. The associated monodromy representations of Artin's braid group capture the essence of the modern view on the subject, which originates in ideas of Riemann and Schwarz. Physically, such monodromy representations correspond to a new type of braid group statistics, which may manifest itself in two-dimensional critical phenomena, e.g. in some exotic quantum Hall states. The associated primary fields satisfy R-matrix exchange relations. The description of the internal symmetry of such fields requires an extension of the concept of a group, thus giving room to quantum groups and their generalizations. We review the appearance of braid group representations in the space of solutions of the Knizhnik - Zamolodchikov equation, with an emphasis on the role of a regular basis of solutions which allows us to treat the case of indecomposable representations as well.

Plenary talk, presented by I. Todorov at XXIII ICGTMP Dubna, July 31 - August 5, 2000 (19 pages, LaTeX, amsfonts, amssymb)

Cited by in corpus (6)

• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Quantum matrix algebra for the SU(n) WZNW model
• Topological Quantum Gates in Homotopy Type Theory
• The origin of multiplets of chiral fields in SU(2)_k WZNW at rational level
• Conformal Geometry and Invariants of 3-strand Brownian Braids
• Braiding Fibonacci anyons