Supersymmetric partition function hierarchies and character expansions

TL;DR

This paper develops supersymmetric deformed partition functions using $W$-representations, explores their character expansions with superpolynomials, and establishes hierarchies and algebraic constraints, advancing the mathematical framework of supersymmetric models.

Contribution

It introduces supersymmetric $eta$ and $(q,t)$-deformed partition functions via $W$-representations and character expansions, and derives their hierarchies and algebraic constraints.

Findings

Constructed supersymmetric deformed partition functions.

Derived super Virasoro constraints and algebraic structures.

Established superintegrability through character expansions.

Abstract

We construct the supersymmetric $\beta$ and $(q,t)$-deformed Hurwitz-Kontsevich partition functions through $W$-representations and present the corresponding character expansions with respect to the Jack and Macdonald superpolynomials, respectively. Based on the constructed $\beta$ and $(q,t)$-deformed superoperators, we further give the supersymmetric $\beta$ and $(q,t)$-deformed partition function hierarchies through $W$-representations. We also present the generalized super Virasoro constraints, where the constraint operators obey the generalized super Virasoro algebra and null super 3-algebra. Moreover, the superintegrability for these (non-deformed) supersymmetric hierarchies is shown by their character expansions, i.e., $<character>\sim character$.