  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 hyperK\"ahler 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, arXiv:1601.05378]. 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.
