A universal formula for deformation quantization on Kähler manifolds

• We give an explicit local formula for any star product with separation of variables.
• Terms of the formula are parametrized by acyclic directed graphs.
• The formula is proved by elementary combinatorial considerations.

We give an explicit local formula for any formal deformation quantization, with separation of variables, on a Kähler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.