Towards testing the Maldacena Conjecture with SDLCQ

TL;DR

This paper tests the Maldacena conjecture for D1-branes using supersymmetric discrete light-cone quantization, providing numerical evidence supporting the conjecture within 10-15% accuracy, but not yet conclusive.

Contribution

It introduces a large-scale numerical approach with enhanced basis reduction techniques to test the conjecture against boundary field theory calculations.

Findings

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

The method scales to approximately 1000 times more states than previous studies.

A new approach using flavor symmetry reduces computational complexity.

Abstract

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and present numerical results of a test of the conjecture against the boundary field theory calculation using supersymmetric discrete light-cone quantization (SDLCQ). We present numerical results with approximately 1000 times as many states as we previously considered. These results support the Maldacena conjecture and are within 10-15% of the predicted numerical results in some regions. Our results are still not sufficient to demonstrate convergence, and, therefore, cannot be considered to a numerical proof of the conjecture. We present a method for using a ``flavor'' symmetry to greatly reduce the size of the basis and discuss a numerical method that we use which is particularly well suited for this type of matrix element calculation.