Alexi Morin-Duchesne ,Centre for Mathematical Physics, Dept of Mathematics , University of Queensland 

The model of critical dense polymers is an integrable model where plane  filling curves are drawn on a lattice and closed contractible loops are disallowed. This model is a particular case of a more general loop model where contractible loops are given a weight beta. In the first part of the seminar, I will explain how lattice loop models appear in the context of phase transitions and why they are interesting from a conformal field theory point of view.

The second part of the talk will be devoted to the description of the model of critical dense polymers on the torus. There, the physical features of the model are encoded in a transfer matrix tangle that lives in the periodic Temperley-Lieb algebra. I will describe how a gluing operator can be used to calculate the partition function on the torus. In a particular case, this partition function turns out to be the modular invariant partition function of symplectic fermions.