Field Theory Correlators and String Theory

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 relating this 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.