Exploring Free Matrix CFT Holographies at One-Loop

TL;DR

This paper investigates the holographic dualities of various free matrix models, extending previous work to new models and computing one-loop energies using a novel method, thereby deepening understanding of higher spin AdS/CFT correspondences.

Contribution

It generalizes the duality analysis to additional free matrix models and introduces the CIRZ method for calculating one-loop energies, addressing ambiguities in the approach.

Findings

Spectrum determined for new models in the planar limit.

One-loop vacuum and Casimir energies computed for dual theories.

Methodological discussion on ambiguities in CIRZ application.

Abstract

We extend our recent study on the duality between stringy higher spin theories and free CFTs in the $SU(N)$ adjoint representation to other matrix models namely the free $SO(N)$ and $Sp(N)$ adjoint models as well as the free $U(N)\times U(M)$ bi-fundamental and $O(N)\times O(M)$ bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we compute the one loop vacuum energy and Casimir energy for their respective bulk duals by means of the CIRZ method that we have introduced recently. We also elaborate on possible ambiguities in the application of this method.