Embedding of bases: from the M(2,2k+1) to the M(3,4k+2-delta) models

TL;DR

This paper introduces a new quasi-particle basis for M(3,p) models that embeds M(2,2k+1) models into M(3,4k+2-delta) models, providing fermionic character formulas and insights into model embeddings.

Contribution

It presents a novel quasi-particle basis for M(3,p) models that reveals an embedding of M(2,2k+1) into M(3,4k+2-delta) models at the basis level.

Findings

Fermionic expressions for M(3,p) characters derived

Embedding of M(2,2k+1) into M(3,4k+2-delta) models demonstrated

New basis formulated using Virasoro and phi_{2,1} modes

Abstract

A new quasi-particle basis of states is presented for all the irreducible modules of the M(3,p) models. It is formulated in terms of a combination of Virasoro modes and the modes of the field phi_{2,1}. This leads to a fermionic expression for particular combinations of irreducible M(3,p) characters, which turns out to be identical with the previously known formula. Quite remarkably, this new quasi-particle basis embodies a sort of embedding, at the level of bases, of the minimal models M(2,2k+1) into the M(3,4k+2-delta) ones, with 0 \leq delta \leq 3.