Super-quantum curves from super-eigenvalue models

Abstract

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce $\beta$-deformed version of those models, and derive differential equations for associated $\alpha /\beta$-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

60 pages

References in corpus (7)

• Les Houches lectures on matrix models and topological strings
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
• N=1 SUSY Conformal Block Recursive Relations
• Elliptic recurrence representation of the N=1 Neveu-Schwarz blocks
• Higher Equations of Motion in N = 1 SUSY Liouville Field Theory
• The super-Virasoro singular vectors and Jack superpolynomials relationship revisited

Cited by in corpus (12)

• CFT approach to constraint operators for ($\beta$-deformed) hermitian one-matrix models
• Collective excitations at filling factor 5/2: The view from superspace
• Super Quantum Airy Structures
• From CFT to Ramond super-quantum curves
• Supereigenvalue Models and Topological Recursion
• Topological Recursion in The Ramond Sector
• Correlators in the supereigenvalue model in the Ramond sector
• Enumeration of chord diagrams via topological recursion and quantum curve techniques
• Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector
• Airy structures for semisimple Lie algebras
• $\mathcal{N}=1$ Super Topological Recursion
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach