Gauge Theory, Geometry and the Large N Limit

TL;DR

This paper explores the connection between M theory and U(N) gauge theories in the large N limit, revealing nonrenormalization theorems and proposing a relation between different string theory limits.

Contribution

It introduces specific large N limits where supergravity is valid and conjectures a link between two limits of string theories based on these gauge theories.

Findings

Large N limits lead to nonrenormalization theorems.

Leading terms in the large N expansion form a Born-Infeld action.

Compatibility of limits suggests a new relation between string theory regimes.

Abstract

We study the relationship between M theory on a nearly lightlike circle and U(N) gauge theory in p+1 dimensions. We define large N limits of these theories in which low energy supergravity is valid. The regularity of these limits implies an infinite series of nonrenormalization theorems for the gauge theory effective action, and the leading large N terms sum to a Born-Infeld form. Compatibility of two different large N limits that describe the same decompactified M theory leads to a conjecture for a relation between two limits of string theories.