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Summary

After a brief review of scale and conformal symmetry, we develop the basic concepts of two-dimensional conformal field theory in a top-down approach. We define primary and quasi-primary fields and the action of conformal transformations on these fields leads to the Virasoro algebra. Operator product expansions, hermitian conjugation, and the state-operator are discussed in the general setting, while results of the previous chapter are recovered as special cases. Null vectors are discussed to prepare for the later discussion of gauge transformations acting on string states. We give an overview of general results about the properties and classification of two-dimensional CFTs.

Summary

We use the case of a single string coordinate to introduce two-dimensional conformal field theory in a bottom-up approach, emphasising the role of operator product expansions and of the state-operator correspondence.

We show that if ${\mathcal C}$ is a fusion $2$ -category in which the endomorphism category of the unit object is or , then the indecomposable objects of ${\mathcal C}$ form a finite group.

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5 - Two-Dimensional Conformal Field Theories

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4 - The Free Massless Scalar Field on the Complex Plane

Summary

FUSION 2-CATEGORIES WITH NO LINE OPERATORS ARE GROUPLIKE

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3 results

5 - Two-Dimensional Conformal Field Theories

Summary

4 - The Free Massless Scalar Field on the Complex Plane

Summary

FUSION 2-CATEGORIES WITH NO LINE OPERATORS ARE GROUPLIKE