Constructive Matrix Theory

We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a non-perturbative construction of the $\phi^{\star 4}_4$ field theory on the Moyal four dimensional space.Comment: 12 pages, 3 figure

Quasiclassical Random Matrix Theory

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, the prime quasiclassical information bearing on the spectrum. The results largely agree with expectations but contain novel features differing from other recent theories.Comment: 4 pages, RevTex, submitted to Phys. Rev. Lett., permanent e-mail [email protected]

Matrix theory of gravitation

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (sec. 4.1). For the standard test cases (PPN scheme, Schwarzschild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.Comment: 24 page

The Matrix Theory S-Matrix

The technology required for eikonal scattering amplitude calculations in Matrix theory is developed. Using the entire supersymmetric completion of the v^4/r^7 Matrix theory potential we compute the graviton-graviton scattering amplitude and find agreement with eleven dimensional supergravity at tree level.Comment: 10 pages, RevTeX, no figure

Why Matrix Theory is Hard

Recently Sen and Seiberg gave a prescription for constructing the matrix theory in any superstring background. We use their prescription to test the finite N matrix theory conjecture on an ALE space. Based on our earlier work with Shenker, we find a sharper discrepancy between matrix theory computation and supergravity prediction. We discuss subtleties in the light-front quantization which may lead to a resolution to the discrepancy.Comment: 10 pages, harvmac; references added, minor correction

Developments in Random Matrix Theory

In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.Comment: 22 pages, Late

Black Holes in Matrix Theory

We review recent progress in understanding black hole structure and dynamics via matrix theory.Comment: 7 pages, latex; (uses espcrc2.sty). Talk by the second author, presented at STRINGS97 (Amsterdam, June 16-20, 1997)