Discretely Holomorphic Observable and its connection with Integrability
by Maria Tsarenko
Abstract: In this talk I will review the construction of the dense loop representation of the Q-state Potts model in two dimensions and consider a parafermionic lattice observable F(z) in this loop formulation. For a particular embedding of the lattice in the plane, I will show that this observable is discretely holomorphic when the Boltzmann weights satisfy certain linear constrains.
Finally, in the case considered, it is observed that discrete holomorphicity holds precisely when the Boltzmann weights lie on the integrable manifold, that is to say, they satisfy the Yang-Baxter equation at criticality, (where the spectral parameter is related linearly to the angle of the elementary plaquette in the embedding).