Interpolation categories for conformal embeddings
Cain Edie‐Michell, Noah Snyder
Source abstract
Abstract In this paper, we give a diagrammatic description of the categories of modules coming from the conformal embeddings . A small variant of this construction (morally corresponding to a conformal embedding of level into level 1) has uniform generators and relations which are rational functions in , which allows us to construct a new continuous family of tensor categories at noninteger level which interpolate between these categories. This is the second example of such an interpolation category for families of conformal embeddings after Zhengwei Liu's interpolation categories which he constructed using his classification of Yang–Baxter planar algebras. Our approach is different from Liu's, we build a two‐color skein theory, with one strand coming from the image of defining representation of and the other strand coming from an invertible object in the category of local modules, and a trivalent vertex coming from a map . We anticipate small variations on our approach will yield interpolation categories for every infinite discrete family of conformal embeddings.
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