Free Large N Supersymmetric Yang-Mills Theory as a String Theory

TL;DR

This paper explores the spectrum of free N=4 super-Yang-Mills theory in the context of the AdS/CFT correspondence, revealing new massless states and confirming duality properties in a tensionless string limit.

Contribution

It investigates the low-lying spectrum of free SYM theory at zero coupling, identifying states absent at strong coupling and analyzing their implications for string theory duals.

Findings

Discovery of massless spin two particles in the spectrum

Conformal dimensions are N-independent in free SYM

Verification of CFT crossing symmetry in the dual model

Abstract

The strong version of Maldacena's AdS/CFT conjecture implies that the large N expansion of free N=4 super-YM theory describes an interacting string theory in the extreme limit of high spacetime curvature relative to the string length. String states may then be understood as composed of SYM string bits. We investigate part of the low-lying spectrum of the tensionless (zero-coupling) limit and find a large number of states that are not present in the infinite tension (strong-coupling) limit, notably several massless spin two particles. We observe that all conformal dimensions are N-independent in the free SYM theory, implying that masses in the corresponding string theory are unchanged by string interactions. Degenerate string states do however mix in the interacting string theory because of the complicated N-dependence of general CFT two-point functions. Finally we verify the CFT crossing symmetry, which corresponds to the dual properties of string scattering amplitudes. This means that the SYM operator correlation functions define AdS dual models analogous to the Minkowski dual models that gave rise to string theory.