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.

arXiv comment60 pages

References in corpus (38)

• Topological Strings and Integrable Hierarchies
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Matrix Model Calculations beyond the Spherical Limit
• Hermitean matrix model free energy: Feynman graph technique for all genera
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Les Houches lectures on matrix models and topological strings
• Quantum Geometry of Refined Topological Strings
• A & B model approaches to surface operators and Toda theories
• Superstring Perturbation Theory Revisited
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
• Matrix eigenvalue model: Feynman graph technique for all genera
• Super-A-polynomial for knots and BPS states
• A-polynomial, B-model, and Quantization
• Higher Equations of Motion in Liouville Field Theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Superloop Equations and Two Dimensional Supergravity
• Sigma-models having supermanifolds as target spaces
• Nonperturbative Solution of the Super-Virasoro Constraints
• Quantum Curves and D-Modules
• Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
• Supermoduli Space Is Not Projected
• Fermionic Matrix Models
• Quantum spectral curve for the Gromov-Witten theory of the complex projective line
• New Geometrical Approach to Superstrings
• N=1 SUSY Conformal Block Recursive Relations
• Decorated Super-Teichmüller Space
• Superconformal field theory and Jack superpolynomials
• Elliptic recurrence representation of the N=1 Neveu-Schwarz blocks
• Super Elliptic Curves
• Higher Equations of Motion in N = 1 SUSY Liouville Field Theory
• Supereigenvalue Model and Dijkgraaf-Vafa Proposal
• Quantum curves and conformal field theory
• Quantum curves
• Supersymmetric Generalizations of Matrix Models
• The super-Virasoro singular vectors and Jack superpolynomials relationship revisited
• Fusion and the Neveu-Schwarz Singular Vectors
• Matrix model with superconformal symmetry

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