Towards a SDLCQ test of the Maldacena conjecture

We consider the Maldacena conjecture applied to the near horizon geometry o f a D1-brane in the supergravity approximation and present numerical result s 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, Po lyakol, and Witten were used. On the field theory side, we derived an expli cit expression for the two-point function in terms of data that may be extr acted from the supersymmetric discrete light cone quantization (SDLCQ) calc ulation at a given harmonic resolution. This yielded a well defined numeric al algorithm for computing the two-point function. For the supersymmetric Y ang-Mills theory with 16 supercharges that arises in the Maldacena conjectu re, the algorithm is perfectly well defined; however, the size of the numer ical computation prevented us from obtaining a numerical check of the conje cture. We now present numerical results with approximately 1000 times as ma ny 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 s ize of the basis and discuss a numerical method that we use which is partic ularly well suited for this type of matrix element calculation. (C) 2000 El sevier Science B.V. All rights reserved.