Singular vector structure of quantum curves

TL;DR

This paper demonstrates that quantum curves are structured as singular vectors within relevant symmetry algebras, linking their formation to topological recursion and introducing super-quantum curves in super-Virasoro contexts.

Contribution

It reveals the singular vector structure of quantum curves across different models and introduces the concept of super-quantum curves, expanding the understanding of quantum curve symmetries.

Findings

Quantum curves form infinite families with singular vector structures.

In the Virasoro case, quantum curves relate to topological recursion.

Introduction of super-quantum curves for super-Virasoro models.

Abstract

We show that quantum curves arise in infinite families and have the structure of singular vectors of a relevant symmetry algebra. We analyze in detail the case of the hermitian one-matrix model with the underlying Virasoro algebra, and the super-eigenvalue model with the underlying super-Virasoro algebra. In the Virasoro case we relate singular vector structure of quantum curves to the topological recursion, and in the super-Virasoro case we introduce the notion of super-quantum curves. We also discuss the double quantum structure of the quantum curves and analyze specific examples of Gaussian and multi-Penner models.