Field Theory Correlators and String Theory

TL;DR

This paper investigates the validity of the Maldacena conjecture by numerically evaluating gauge-invariant correlators in supersymmetric Yang-Mills theories in two and three dimensions, supporting the duality with gravity.

Contribution

It provides the first non-perturbative numerical evidence supporting the Maldacena conjecture in 2D SYM using SDLCQ and extends analysis to 3D N=1 SYM, exploring correlators without known gravity duals.

Findings

Numerical results support the Maldacena conjecture within 10-15%.

Correlators in 2D SYM match supergravity predictions.

Analysis of 3D N=1 SYM reveals BPS state information.

Abstract

It appears that string-M-theory is the only viable candidate for a complete theory of matter. It must therefore contain both gravity and QCD. What is particularly surprising is the recent conjecture that strongly coupled QCD matrix elements can be evaluated though a duality with weakly coupled gravity. To date there has been no direct verification of this conjecture by Maldacena because of the difficulty of direct strong coupling calculations in gauge theories. We report here on some progress in evaluating a gauge-invariant correlator in the non-perturbative regime in two and three dimensions in SYM theories. The calculations are made using supersymmetric discrete light-cone quantization (SDLCQ). We consider a Maldacena-type conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation, solve the corresponding N=(8,8) SYM theory in two dimensions, and evaluate the correlator of the stress-energy tensor. Our numerical results support the Maldacena conjecture and are within 10-15% of the predicted results. We also present a calculation of the stress-energy correlator in N=1 SYM theory in 2+1 dimensions. While there is no known duality relatingthis theory to supergravity, the theory does have massless BPS states, and the correlator gives important information about the BPS wave function in the non-perturbative regime.