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Super-quantum curves from super-eigenvalue models
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DOI：10.1007/JHEP10(2016)044.png)
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Abstract
En 中文
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.
Keywords:
Matrix Models
Conformal and W Symmetry
2D Gravity
Topological Strings
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