Secondary invariants and non-perturbative states

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Abstract
A bstract: At finite N the ring of gauge invariant operators is not freely generated. For problems of interest in physics, these rings are Cohen-Macaulay and admit a Hironaka decomposition, in which the full invariant ring is a free module over a polynomial ring generated by the primary invariants. The module basis is given by finitely many secondary invariants. This motivates a physical picture in which the primary invariants are regarded as perturbative degrees of freedom while the secondary invariants are associated with distinguished non-perturbative states or sectors. The purpose of this study is to show that a concrete algebraic version of this picture is visible in simple zero-dimensional matrix integrals.
Funding Information
  • National Research Foundation (65212)

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