Refined conformal spectra in the dimer model

TL;DR

This paper analyzes the dimer model's transfer matrix, revealing sector structures linked to conformal field theories with central charge c=-2, and connects these findings to the critical dense polymer model.

Contribution

It introduces a sector decomposition of the dimer model based on a variation index and relates these sectors to Virasoro algebra representations in the continuum limit.

Findings

Identification of sectors labeled by variation index

Derivation of conformal partition functions for each sector

Connection to Ramond and Neveu-Schwarz sectors of dense polymers

Abstract

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu-Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c=-2.