Dimer Models, Free Fermions and Super Quantum Mechanics

Understand

This note relates topics in statistical mechanics, graph theory and combinatorics, lattice quantum field theory, super quantum mechanics and string theory.

• We give a precise relation between the dimer model on a graph embedded on a torus and the massless free Majorana fermion living on the same lattice.
• A loop expansion of the fermion determinant is performed, where the loops turn out to be compositions of two perfect matchings.
• These loop states are sorted into co-chain groups using categorification techniques similar to the ones used for categorifying knot polynomials.