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arXiv · 2608.22952

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

Robert de Mello Koch·Minkyoo Kim·Augustine Larweh Mahu·Anik Rudra
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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}

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Robert de Mello Koch, Minkyoo Kim, Augustine Larweh Mahu, Anik Rudra. 2026-08-24. A pedagogical introduction to invariant theory and finite-$N$ holography. https://arxiv.org/abs/2608.22952

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