Towards a SDLCQ test of the Maldacena Conjecture

TL;DR

This paper tests the Maldacena conjecture by numerically comparing supergravity predictions with boundary field theory calculations using SDLCQ, achieving results supporting the conjecture within 10-15% accuracy.

Contribution

It introduces an improved numerical approach with larger state spaces to test the conjecture, providing partial support through approximate numerical results.

Findings

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

A new method reduces basis size using flavor symmetry, enabling larger computations.

Results are close but not conclusive for a full proof of the conjecture.

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 DLCQ. We previously calculated the two-point function of the stress-energy tensor on the supergravity side; the methods of Gubser, Klebanov, Polyakov, and Witten were used. On the field theory side, we derived an explicit expression for the two-point function in terms of data that may be extracted from the supersymmetric discrete light cone quantization (SDLCQ) calculation at a given harmonic resolution. This yielded a well defined numerical algorithm for computing the two-point function. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined; however, the size of the numerical computation prevented us from obtaining a numerical check of the conjecture. We now 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.