Title: Extensions of modular tensor categories and subtheories in conformal field theory
Speaker: Marcel Bischoff (Vanderbilt University)
Abstract: From a commutative algebra object in a (unitary) modular tensor category, one gets a new (smaller) modular tensor category of dyslectic modules. This process correspond to extensions in rational conformal field theory or condensation in topological phases of matter. In particular, one can study extensions in rational conformal field theory from a purely categorical point of view. Conversely, passing to a subtheory, one gets a bigger modular tensor category. But knowing only the modular tensor category C is not enough to determine the possible modular tensor categories of subtheories of a given theory realizing C. Therefore on the categorical level one only gets necessary restrictions, whose structure I will discuss. Further, I will discuss examples coming from near group categories, which give the existence of interesting (often still hypothetical) subtheories of conformal field theories whose representation categories are pointed modular tensor categories.