Short Star-Products for Filtered Quantizations, I
Abstract
We develop a theory of short star-products for filtered quantizations of graded Poisson algebras, introduced in 2016 by Beem, Peelaers and Rastelli for algebras of regular functions on hyperKähler cones in the context of 3-dimensional $N=4$ superconformal field theories [Beem C., Peelaers W., Rastelli L., Comm. Math. Phys. 354 (2017), 345-392]. This appears to be a new structure in representation theory, which is an algebraic incarnation of the non-holomorphic ${\rm SU}(2)$-symmetry of such cones. Using the technique of twisted traces on quantizations (an idea due to Kontsevich), we prove the conjecture by Beem, Peelaers and Rastelli that short star-products depend on finitely many parameters (under a natural nondegeneracy condition), and also construct these star products in a number of examples, confirming another conjecture by Beem, Peelaers and Rastelli.
- Publication:
-
SIGMA
- Pub Date:
- March 2020
- DOI:
- arXiv:
- arXiv:1909.13588
- Bibcode:
- 2020SIGMA..16..014E
- Keywords:
-
- star-product; quantization; hyperKähler cone; symplectic singularity;
- Mathematics - Representation Theory;
- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Quantum Algebra
- E-Print:
- SIGMA 16 (2020), 014, 28 pages