Super-quantum curves from super-eigenvalue models
- First Online:
- Cite this article as:
- Ciosmak, P., Hadasz, L., Manabe, M. et al. J. High Energ. Phys. (2016) 2016: 44. doi:10.1007/JHEP10(2016)044
- 54 Downloads
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 β-deformed version of those models, and derive differential equations for associated α/β-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.