SM(2,4k) fermionic characters and restricted jagged partitions

TL;DR

This paper derives a basis for states in SM(2,4k) superconformal models using null fields, expressing it through exclusion conditions linked to jagged partitions, and provides new fermionic character formulas.

Contribution

It introduces a novel quasi-particle basis for SM(2,4k) models based on null field hypotheses and connects it to restricted jagged partitions for character computation.

Findings

Derived a basis expressed via G_r modes and exclusion conditions.

Established correspondence with (2k-1)-restricted jagged partitions.

Provided new fermionic formulas for characters in both sectors.

Abstract

A derivation of the basis of states for the $SM(2,4k)$ superconformal minimal models is presented. It relies on a general hypothesis concerning the role of the null field of dimension $2k-1/2$. The basis is expressed solely in terms of $G_r$ modes and it takes the form of simple exclusion conditions (being thus a quasi-particle-type basis). Its elements are in correspondence with $(2k-1)$-restricted jagged partitions. The generating functions of the latter provide novel fermionic forms for the characters of the irreducible representations in both Ramond and Neveu-Schwarz sectors.