  In this paper we show how Einstein metrics are naturally described using the
quantization of the algebra of functions on a Kahler manifold M. In this setup
one interprets M as the phase space itself, equipped with the Poisson brackets
inherited from the Kahler 2-form. We compare the geometric quantization
framework with several deformation quantization approaches. We find that the
balanced metrics appear naturally as a result of setting the vacuum energy to
be the constant function on the moduli space of semiclassical vacua. In the
classical limit these metrics become Kahler-Einstein (when M admits such
metrics). Finally, we sketch several applications of this formalism, such as
explicit constructions of special Lagrangian submanifolds in compact Calabi-Yau
manifolds.
