Abstract: |
(Chiral) conformal field theory and its axiomatisation, vertex algebras, are a rich source of interesting tensor categories through their representation theory. A common assumption when studying vertex algebras is rationality, which in particular implies that their representation categories are modular tensor categories and hence come with a notion of duality (akin to taking duals of vector spaces) called rigidity. In practice rigidity is an extremely difficult property to verify, as can be seen from Huang's proof of the Verlinde conjecture or from the fact that there are very few rigidity results outside of rationality. This is because general vertex algebra representation categories need not be rigid, however, they do satisfy a weaker duality structure called Grothendieck-Verdier duality, which I shall explain in this talk and illustrate through the example of the free boson (a.k.a the Heisenberg vertex algebra). |