From CFT to Ramond super-quantum curves

Abstract

As we have shown in the previous work, using the formalism of matrix and eigenvalue models, to a given classical algebraic curve one can associate an infinite family of quantum curves, which are in one-to-one correspondence with singular vectors of a certain (e.g. Virasoro or super-Virasoro) underlying algebra. In this paper we reformulate this problem in the language of conformal field theory. Such a reformulation has several advantages: it leads to the identification of quantum curves more efficiently, it proves in full generality that they indeed have the structure of singular vectors, it enables identification of corresponding eigenvalue models. Moreover, this approach can be easily generalized to other underlying algebras. To illustrate these statements we apply the conformal field theory formalism to the case of the Ramond version of the super-Virasoro algebra. We derive two classes of corresponding Ramond super-eigenvalue models, construct Ramond super-quantum curves that have the structure of relevant singular vectors, and identify underlying Ramond super-spectral curves. We also analyze Ramond multi-Penner models and show that they lead to supersymmetric generalizations of BPZ equations.

72 pages

References in corpus (5)

• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Super-quantum curves from super-eigenvalue models
• Integrable differential systems of topological type and reconstruction by the topological recursion
• The super-Virasoro singular vectors and Jack superpolynomials relationship revisited
• Quantizing Weierstrass

Cited by in corpus (9)

• CFT approach to constraint operators for ($\beta$-deformed) hermitian one-matrix models
• Super Quantum Airy Structures
• Topological Recursion in The Ramond Sector
• Correlators in the supereigenvalue model in the Ramond sector
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector
• $\mathcal{N}=1$ Super Topological Recursion
• Airy structures for semisimple Lie algebras
• Analyticity of the free energy for quantum Airy structures