Consistency conditions in the chiral ring of super-Yang-Mills theories

Starting from the generalized Konishi anomaly equations at the non-perturbative level, we demonstrate that the algebraic consistency of the quantum chiral ring of the N=1 super-Yang-Mills theory with gauge group U(N), one adjoint chiral superfield X and Nf⩽2N flavours of quarks implies that the periods of the meromorphic one-form Trdzz−X must be quantized. This shows in particular that identities in the open string description of the theory, that follow from the fact that gauge invariant observables are expressed in terms of gauge variant building blocks, are mapped onto non-trivial dynamical equations in the closed string description.