Work

From symmetry to structure: gauge-invariant operators in multi-matrix quantum mechanics

Year: 2026

Type: article

Abstract: A bstract Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the module structure is determined by a finite set of secondary invariants. In this work, we show that the number of primary invariants can be computed by performing a complete gauge fixing, which identifies the number of independent physical degrees of freedom. We then compare this result to a complementary counting based on the restricted Schur polynomial basis. This comparison allows us to argue that the number of secondary invariants must exhibit exponential growth of the form $${e}^{c{N}^{2}}$$ at large N , with c a constant.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep01(2026)031

Authors: Robert de Mello Koch, Minkyoo Kim, Hendrik J. R. Van Zyl

Institutions: University of the Witwatersrand, Huzhou Normal University, Sogang University, University of Cape Town

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Huzhou University, National Research Foundation of Korea

Awards: G6159057712, G7497519523, G8516841700