The Chiral Ring and the Periods of the Resolvent

Abstract

The strongly coupled vacua of an N=1 supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated N=2 Seiberg-Witten curve (the so-called strong-coupling approach). We show that these conditions are equivalent to the existence of certain relations in the chiral ring, which themselves follow from the fact that the gauge group has a finite rank. This provides a conceptually very simple explanation of why and how the strongly coupled physics of N=1 theories, including fractional instanton effects, chiral symmetry breaking and confinement, can be derived from purely semi-classical calculations involving instantons only.

arXiv comment17 pages, 1 figure; v2: cosmetic changes

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Cited by in corpus (13)

• Extended N=1 super Yang-Mills theory
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Consistency conditions in the chiral ring of super Yang-Mills theories
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials
• Microscopic quantum superpotential in N=1 gauge theories
• Glueball operators and the microscopic approach to N=1 gauge theories
• Effective superpotential and partial breaking of N=2 supersymmetry
• The Microscopic Approach to N=1 Super Yang-Mills Theories
• N=1* model superpotential revisited (IR behaviour of N=4 limit)
• Flavors in the microscopic approach to N=1 gauge theories
• SUSY/Non-SUSY Duality in U(N) Gauge Model with Partially Broken N=2 Supersymmetry
• On the Chiral Ring and Vacua of $\mathcal{N}=1$ Adjoint SQCD