Boundary Conformal Field Theory, Fusion Ring Representations and Strings
We'll begin with a gentle overview, discussing some of the background
context. This will include some words on Monstrous Moonshine, modular
functions, (boundary) conformal field theory, and string theory. Then
we'll
turn to fusion rings and the basic partition functions of the theory,
where
much of the data of the theory is conveniently encoded. We'll focus on
the partition function of the torus (relevant to closed string theory,
or the CFT of the bulk) and that of the cylinder (which is relevant to
open string theory and boundary CFT).
References:
Although not strictly necessary, it would be convenient for the audience
to
have some familiarity with the elementary representation theory of affine
Kac-Moody algebras, and also the elementary theory of modular forms. These
are
reviewed for instance in the textbooks
- Fuchs, Schweigert, ``Symmetries, Lie algebras and representations'',
- Miyake, ``Modular forms''
although there are several other sources.
More specific background for my lectures is provided for instance by:
- Zuber, `CFT, BCFT, ADE and all that', hep-th/0006151;
- Gannon, `Monstrous moonshine and the classification of CFT',
math.QA/9906167;
- Schweigert, Fuchs, Walcher, `Conformal field theory, boundary
conditions
and
applications to string theory' hep-th/0011109.