Please note: You are viewing the unstyled version of this web site. Either your browser does not support CSS (cascading style sheets) or it has been disabled.

Macquarie University  Department of Mathematics

Local Navigation

Categories in Algebra, Geometry and Mathematical Physics

Conference in honour of Ross Street's sixtieth birthday

July 11-16 2005, Macquarie University, Sydney

Tue, 12 July:  15:20 - 16:00

Conformal field theory and Frobenius algebras in modular tensor categories
Fuchs, Jürgen (Karlstads Universitet, Sweden)

A class of Frobenius algebras in modular tensor categories provides the right tools for proving the existence of two-dimensional rational conformal quantum field theories. For an algebra $A$ in this class, the construction used in the proof provides in particular a dictionary between algebraic structures and physical concepts, part of which looks as follows:\\[1ex]
category of left $A$-modules &= &boundary conditions \\[.5ex]
category of $A$-bimodules &= &defect lines \\[.5ex]
bimodule morphisms between
certain induced bimodules &= &bulk fields \\[.5ex]
Picard group of the
bimodule category &= &internal symmetries
Morita-equivalent algebras yield the same conformal field theory; the Brauer group of the modular tensor category describes the subset of modular invariant partition functions that arise from an automorphism of the fusion rules.

Typeset PDF of this abstract.