The Chiral Ring and the Periods of the Resolvent

Frank Ferrari

doi:10.1016/j.nuclphysb.2007.02.018

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arXiv · hep-th/0701220

The Chiral Ring and the Periods of the Resolvent

Frank Ferrari

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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.

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Frank Ferrari. 2007-03-19. The Chiral Ring and the Periods of the Resolvent. https://doi.org/10.1016/j.nuclphysb.2007.02.018

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