A bijection between paths for the M(p,2p+1) minimal model Virasoro characters

TL;DR

This paper establishes a bijection between two different path representations of states in the M(p,2p+1) minimal model Virasoro modules, confirming the correctness of a new half-integer lattice path approach.

Contribution

It introduces and proves a bijection between the known integer lattice paths and a new half-integer lattice path representation for M(p,2p+1) models.

Findings

Bijection between two path representations established

Half-lattice path representation for M(p+1,2p+1) models proposed

Differences in fermionic characters resolved

Abstract

The states in the irreducible modules of the minimal models can be represented by infinite lattice paths arising from consideration of the corresponding RSOS statistical models. For the M(p,2p+1) models, a completely different path representation has been found recently, this one on a half-integer lattice; it has no known underlying statistical-model interpretation. The correctness of this alternative representation has not yet been demonstrated, even at the level of the generating functions, since the resulting fermionic characters differ from the known ones. This gap is filled here, with the presentation of two versions of a bijection between the two path representations of the M(p,2p+1) states. In addition, a half-lattice path representation for the M(p+1,2p+1) models is stated, and other generalisations suggested.