Conformal blocks in the large D limit

D-brane Conformal Field Theory and Bundles of Conformal Blocks

Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply a Verlinde formula for non-simply connected groups like PGL(n, C). We then explain how conformal blocks enter in the construction of conformal field theories...

On the Large N Limit of Conformal Field Theory

Following recent advances in largeN matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results is a new affine free algebra which describes a large N limit of su(N) affine Lie algebra. Other results include the associated free-algebraic partition functi...

The Algebra of Conformal Blocks

Abstract. We study and generalize the connection between the phylogenetic Hilbert functions of Buczynska and Wisniewski [BW] and the Verlinde formula, as discovered by Sturmfels and Xu in [StX]. In order to accomplish this we introduce deformations of algebras of non-abelian theta functions for a general simple complex Lie algebra g structured on the moduli stack of stable punctured curves. We ...

D-brane Conformal Eld Theory and Traces on Bundles of Conformal Blocks

Decomposition of Conformal Blocks

In the Masters Project we give a complete proof of the Factorization theorem in Conformal Field Theory and Local freeness of the sheaf of conformal blocks. We apply these results to give a proof of the Verlinde formula. Except for the part on Verlinde formula (Chapter 8), we mostly follow the description given in [TUY]. For the Verlinde formula, we follow the article [Beau]. We do not claim any...