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# Macquarie University  Department of Mathematics

## 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]
\newcommand{\PBS}[1]{\let\temp=\\#1\let\\=\temp}
category of left $A$-modules &= &boundary conditions \\[.5ex]
category of $A$-bimodules &= &defect lines \\[.5ex]