9 papers
Secondary invariants and non-perturbative states
Robert de Mello Koch, João P. Rodrigues
At finite 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…
Finite Hilbert Spaces of Bilocal Holography
Robert de Mello Koch, Antal Jevicki, Junggi Yoon
For vector/AdS and dS holography we establish the structure of the emergent Hilbert space. This is done through implementation of finite trace relations on the infinite collect…
From Symmetry to Structure: Gauge-Invariant Operators in Multi-Matrix Quantum Mechanics
Robert de Mello Koch, Minkyoo Kim, Hendrik J. R. Van Zyl
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…
Gauge Invariants at Arbitrary and Trace Relations
Pawel Caputa, Robert de Mello Koch
We investigate conformal field theories with gauge group at arbitrary rank , focusing on the role of trace relations in determining the structure of the Hilbert space. Wo…
Collective Theory at Finite-: Reduction of the Emergent Hilbert Space
Robert de Mello Koch, Antal Jevicki, Garreth Kemp +1
Continuing the formulation of finite Hilbert spaces in emergent theories we study in this work symmetric collective models. For the case of bosons in dimensions…
Hilbert Space of Finite Multi-matrix Models
Robert de Mello Koch, Antal Jevicki
We study the Hilbert space structure of gauge-invariant operators emergent in large- multi-matrix quantum mechanics. Building on the framework of \cite{deMelloKoch:2025ngs}, we…