  We define a notion of stability for chiral ring of four dimensional N=1
theory by introducing test chiral rings and generalized a maximization. We
conjecture that a chiral ring is the chiral ring of a superconformal field
theory if and only if it is stable. We then study N=1 field theory derived from
D3 branes probing a three-fold singularity X, and show that the K stability
which implies the existence of Ricci-flat conic metric on X is equivalent to
the stability of chiral ring of the corresponding field theory.
