Microscopic Models for Fusion Categories

Understand

This is a PhD Thesis on the connection between subfactors (more precisely, their corresponding fusion categories) and Conformal Field Theory (CFT).

• Besides being a mathematically interesting topic on its own, subfactors have also attracted the attention of physicists, since there is a conjectured correspondence between these and CFTs.
• Although there is quite a persuasive body of evidence for this conjecture, there are some gaps: there exists a set of exceptional subfactors with no known counterpart CFT.
• Hence, it is necessary to develop new techniques for building a CFT from a subfactor.