Discrete symplectic fermions on double dimers and their Virasoro representation

Abstract

A discrete version of the Conformal Field Theory of symplectic fermions is introduced and discussed. Specifically, discrete symplectic fermions are realised as holomorphic observables in the double-dimer model. Using techniques of discrete complex analysis, the space of local fields of discrete symplectic fermions on the square lattice is proven to carry a representation of the Virasoro algebra with central charge $-2$.

34 pages, 13 figures; v2: fermion modes rewritten more meaningful way

References in corpus (2)

• Fourier transform on high-dimensional unitary groups with applications to random tilings
• Tau-functions à la Dubédat and probabilities of cylindrical events for double-dimers and CLE(4)