Gauge Theory, Geometry and the Large N Limit

TL;DR

The paper investigates M-theory on a nearly lightlike circle and its relation to U(N) gauge theory in p+1 dimensions, identifying three large-N limits (L1, L2, L3) that preserve a low-energy supergravity description and yield nonrenormalization theorems for the gauge-theory effective action. It shows that the leading large-N planar diagrams resum into a Born-Infeld form, with independent evidence from short-distance Dp-brane dynamics supporting this BI resummation. A second decompactification limit and a conjectured equivalence between distinct string-theory limits are explored, suggesting that the same decompactified M-theory can be described by different string-theory regimes. The work links gauge-theory loop expansions to 11D supergravity corrections and provides a framework for relating seemingly disparate limits of string theory through M-theory backbones, with implications for holography and the emergence of geometry from gauge dynamics.

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.

Figures (1)

• Figure 1: Two possible decompactification limits