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

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.

26 pages, 1 figure; v2: typos corrected, published version

References in corpus (6)

• A Perturbative Window into Non-Perturbative Physics
• Extended N=1 super Yang-Mills theory
• The Chiral Ring and the Periods of the Resolvent
• The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems
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Cited by in corpus (5)

• Extended N=1 super Yang-Mills theory
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials
• Glueball operators and the microscopic approach to N=1 gauge theories
• On the Chiral Ring and Vacua of $\mathcal{N}=1$ Adjoint SQCD