Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models

TL;DR

This paper develops a nonlocal operator basis from path representations of minimal models, enabling new derivations of characters and extending to related models, thus offering a novel algebraic framework for these conformal theories.

Contribution

It introduces a nonlocal operator basis from path descriptions of minimal models, generalizing to related models and providing a new method to compute characters.

Findings

Constructed a nonlocal operator basis for minimal models.

Derived the vacuum finite fermionic character using the basis.

Extended the approach to models M(k+1,2k+3).

Abstract

We reinterpret a path describing a state in an irreducible module of the unitary minimal model M(k+1,k+2) in terms of a string of charged operators acting on the module's ground-state path. Each such operator acts non-locally on a path. The path characteristics are then translated into a set of conditions on sequences of operators that provide an operator basis. As an application, we re-derive the vacuum finite fermionic character by constructing the generating function of these basis states. These results generalize directly to the M(k+1,2k+3) models, the close relatives of the unitary models in terms of path description.