Can DLCQ test the Maldacena Conjecture?

TL;DR

This paper explores testing the Maldacena conjecture using DLCQ by computing stress energy tensor two-point functions on both supergravity and field theory sides, providing a numerical algorithm and preliminary results for supersymmetric Yang-Mills theories.

Contribution

It introduces a numerical method to compute stress tensor correlators in supersymmetric theories within the DLCQ framework, enabling potential tests of the Maldacena conjecture.

Findings

Algorithm successfully computes correlators for free fermions and 't Hooft model.

Preliminary results obtained for supersymmetric Yang-Mills theories with various supersymmetries.

Growth of computational complexity limits detailed analysis at present.

Abstract

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and consider the possibility of testing the conjecture against the boundary field theory calculation using DLCQ. We propose the two point function of the stress energy tensor as a convenient quantity that may be computed on both sides of the correspondence. On the supergravity side, we may invoke the methods of Gubser, Klebanov, Polyakov, and Witten. On the field theory side, we derive an explicit expression for the two point function in terms of data that may be extracted from a DLCQ calculation at a given harmonic resolution. This gives rise to a well defined numerical algorithm for computing the two point function, which we test in the context of free fermions and the 't Hooft model. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined, although the size of the numerical computation grows too fast to admit any detailed analysis at present, and our results are only preliminary. We are, however, able to present more detailed results on the supersymmetric DLCQ computation of the stress energy tensor correlators for two dimensional Yang Mills theories with (1,1) and (2,2) supersymmetries.