On the definition and K-theory realization of a modular functor

We present a definition of a (super)-modular functor which includes certain interesting cases that previous definitions do not allow. We also introduce a notion of topological twisting of a modular functor, and construct formally a realization by a 2-dimensional topological field theory valued in twisted [Formula: see text]-modules. We discuss, among other things, the [Formula: see text]-supersymmetric minimal models from the point of view of this formalism.

GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16, 19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].

CONSTRUCTING TQFTS FROM MODULAR FUNCTORS

We prove in this paper that any 2 dimensional modular functor satisfying that S1,1≠0 induces a family of 2+1 dimensionally topological quantum field theories. We do this for two kinds of modular functors namely a modular functor on the category of extended surfaces and a modular functor on the category of extended surfaces with marked points and directions. We follow the ideas of M. Kontsevich, [21], and K. Walker, [32] but we give proofs and provide details left out in [21] and [32]. Careful study also shows that more choices are needed to define the TQFT than it is revealed in [21] and [32]. On the other hand, relations found in [32] turns out not to be needed here.

SL(2, C)-TOPOLOGICAL QUANTUM FIELD THEORY WITH CORNERS

In this paper we define the sl(2, C) topological quantum field theory with corners that corresponds to the smooth theory of Reshetikhin and Turaev. We encounter a sign obstruction at the level of the modular functor, which we solve by making use of the Klein four group. We deduce the Moore-Seiberg equations in the new context.