Seminar detail: The space of gauge invariant operators at finite N

Date&Time	Tue Oct 21 2025 (17:00 - 18:00)
Speaker	Robert de Mello Koch
Affiliation	Huzhou U
Title	The space of gauge invariant operators at finite N
Abstract	We argue that the space of invariants of multi-matrix model quantum mechanics, at finite N, is generated by a set of invariants, naturally divided into two distinct classes: primary and secondary. The primary invariants act freely, while secondary invariants satisfy quadratic relations. Significantly, while traces with at most N matrices are always present, we also find invariants involving more than N matrices per trace. We argue that the primary invariants correspond to perturbative degrees of freedom, whereas the secondary invariants emerge as non-trivial background structures. The number of primary invariants for a model with d matrices is given by 1+(d-1)N^2. By comparing the Molien-Weyl partition function to a complementary counting based on the restricted Schur polynomials we argue that the number of secondary invariants grows as e^{cN^2} at large N, with c a constant. Finally, we identify a class of light single-trace operators that behave like free creation operators at low energy but saturate beyond a critical excitation level, ceasing to generate new states. This reducibility is a direct consequence of finite N trace identities and leads to a dramatic truncation of the high-energy spectrum of the emergent theory. The resulting number of independent degrees of freedom is far smaller than naïve semiclassical expectations, providing a concrete mechanism for how nonperturbative constraints shape the ultraviolet behaviour of emergent theories.
Remarks	Online talk
Slide/Video	slide1