Secondary invariants and non-perturbative states
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.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Advanced Operator Algebra Research
Publication details
- Journal / source
- Journal of High Energy Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 6
- Publication date
- 25 June 2026
- Language
- EN