String Expansion as Large N Expansion of Gauge Theories

TL;DR

This paper demonstrates that string perturbation theory with D-branes in orbifolded space-time aligns with 't Hooft's large N expansion, and proves all-order vanishing of beta functions in certain supersymmetric theories.

Contribution

It establishes a connection between string perturbation theory and large N gauge theories, proving all-order beta function vanishing theorems using world-sheet orbifold techniques.

Findings

String perturbation matches large N expansion in orbifolded backgrounds.

All-order vanishing of beta functions for certain supersymmetric theories.

Supports recent predictions about gauge/string duality.

Abstract

We consider string perturbative expansion in the presence of D-branes imbedded in orbifolded space-time. In the regime where the string coupling is weak and $\alpha'\to 0$, the string perturbative expansion coincides with `t Hooft's large N expansion. We specifically concentrate on theories with d=4 and ${\cal N}=0,1,2,4$, and use world-sheet orbifold techniques to prove vanishing theorems for the field theory beta functions to all orders in perturbation theory in the large N limit. This is in accord with recent predictions.