Singular vector structure of quantum curves
High Energy Physics - Theory
2017-11-23 v1 Mathematical Physics
math.MP
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1711.08031,
title = {Singular vector structure of quantum curves},
author = {Paweł Ciosmak and Leszek Hadasz and Masahide Manabe and Piotr Sułkowski},
journal= {arXiv preprint arXiv:1711.08031},
year = {2017}
}
Comments
33 pages; proceedings of the 2016 AMS von Neumann Symposium