# Contents

## Idea

The local data for a CFT in dimension $d$ allows to assign to each $d$-dimensional cobordism $\Sigma$ a vector space of “possible correlator”s: those functions on the space of conformal structures on $\Sigma$ that have the correct behaviour to qualify as the (chiral) correlator of a CFT. This is called a space of conformal blocks $\mathrm{Bl}\left(\Sigma \right)$. This assignment is functorial under diffeomorphism. The corresponding functor is called a modular functor.

To get an actual collection of correlators one has to choose from each space of conformal blocks $\mathrm{Bl}\left(\Sigma \right)$ an element such that these choices glue under composition of cobordism: such that they solve the sewing constraints.

## References

A generalization of the modular functors is in

• Igor Kriz, Luhang Lai, On the definition and K-theory realization of a modular functor, arxiv/1310.5174

Revised on October 22, 2013 05:03:26 by Zoran Škoda (161.53.130.104)