Work

A pedagogical introduction to invariant theory and finite-$N$ holography

Year: 2026

Type: preprint

Abstract: These lectures provide a pedagogical introduction to the study of finite-$N$ physics of the AdS/CFT correspondence. More specifically we develop the consequences of the trace relations for the space of gauge invariant operators, using powerful methods from invariant theory. Our key conclusions are \begin{itemize} \item that the complete set of trace relations can be solved, leaving a non-redundant set of gauge invariant operators, \item that this non-redundant set can be generated using two types of generators, called primary and secondary invariants, and \item that the primary invariants acquire a natural interpretation as perturbative gravitational degrees of freedom, while the secondary algebra encodes non-perturbative effects of the dual gravitational theory. \end{itemize}

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.22952

Authors: Koch, Robert de Mello, Kim, Minkyoo, Mahu, Augustine Larweh, Rudra, Anik

Institutions: Seoul National University, Huzhou Normal University, University of Ghana, University of the Witwatersrand

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Kyung Hee University, Ministry of Science and ICT, South Korea

OpenAlex ID: W7204189889

Cites: 59

Cited by: 6

Related to: 10