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

TL;DR

This paper shows that the algebraic consistency of the quantum chiral ring in certain super Yang-Mills theories requires the quantization of periods of a meromorphic one-form, linking open and closed string descriptions.

Contribution

It establishes a connection between the consistency conditions of the chiral ring and the quantization of periods, providing new insights into non-perturbative dynamics of super Yang-Mills theories.

Findings

Quantization of periods of meromorphic one-form is necessary for chiral ring consistency.

Open string identities correspond to dynamical equations in the closed string framework.

Demonstrates the algebraic constraints arising from generalized Konishi anomaly equations.

Abstract

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 N_f<=2N flavours of quarks implies that the periods of the meromorphic one-form Tr dz/(z-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.