Renormalization of Higher Derivative Operators in the Matrix Model

TL;DR

This paper investigates the renormalization properties of higher derivative operators in matrix models related to M-theory, providing evidence for non-renormalization theorems at certain orders and highlighting limitations at higher orders.

Contribution

It offers new insights into the non-renormalization of specific terms in matrix models of M-theory, especially for low-dimensional cases, and clarifies the scope of protected quantities.

Findings

Non-renormalization theorems hold for v^4 terms in 0+1 and 1+1 dimensions.

Evidence suggests no non-renormalization theorems for v^8 and higher orders.

Results clarify the conditions under which matrix models accurately describe M-theory quantities.

Abstract

$M$-theory is believed to be described in various dimensions by large $N$ field theories. It has been further conjectured that at finite $N$, these theories describe the discrete light cone quantization (DLCQ) of $M$ theory. Even at low energies, this is not necessarily the same thing as the DLCQ of supergravity. It is believed that this is only the case for quantities which are protected by non-renormalization theorems. In 0+1 and 1+1 dimensions, we provide further evidence of a non-renormalization theorem for the $v^4$ terms, but also give evidence that there are not such theorems at order $v^8$ and higher.