On the Supergravity Gauge theory Correspondence and the Matrix Model

TL;DR

This paper reviews the derivation and validity of DLCQ Matrix models, their relation to supergravity and AdS/CFT duality, and clarifies the roles of non-renormalization theorems and higher order corrections.

Contribution

It clarifies the assumptions and limitations of DLCQ Matrix models and compares their relation to supergravity and Maldacena's conjecture, especially in finite N regimes.

Findings

Finite N effects in DLCQ Matrix models analyzed

Comparison between Matrix model compactification and AdS/CFT duality

Role of branes in different duality contexts explained

Abstract

We review the assumptions and the logic underlying the derivation of DLCQ Matrix models. In particular we try to clarify what remains valid at finite $N$, the role of the non-renormalization theorems and higher order terms in the supergravity expansion. The relation to Maldacena's conjecture is also discussed. In particular the compactification of the Matrix model on $T_3$ is compared to the $AdS_5\times S_5$ ${\cal N}=4$ super Yang-Mills duality, and the different role of the branes in the two cases is pointed out.