Title: Non-perturbative structure from invariant theory

Abstract: At finite N the ring of gauge invariant operators is not freely generated. However, 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. This talk will show that a concrete algebraic version of this picture is already visible in simple zero-dimensional matrix integrals.