Dimer Models, Free Fermions and Super Quantum Mechanics

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dc.creatorDijkgraaf, R.
dc.creatorOrlando, D.
dc.creatorReffert, S.
dc.date2007-05-11
dc.date2007-11-12
dc.date.accessioned2026-07-07T08:41:44Z
dc.date.available2026-07-07T08:41:44Z
dc.descriptionThis 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. The Euler characteristic of the resulting co-chain complex recovers the Newton polynomial of the dimer model. We re-interpret this system as supersymmetric quantum mechanics, where configurations with vanishing net winding number form the ground states. Finally, we make use of the quiver gauge theory - dimer model correspondence to obtain an interpretation of the loops in terms of the physics of D-branes probing a toric Calabi-Yau singularity.
dc.descriptionminor corrections, reference added
dc.identifierhttps://arxiv.org/abs/0705.1645
dc.identifierhttp://arxiv.org/abs/0705.1645
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141768
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleDimer Models, Free Fermions and Super Quantum Mechanics
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