ar X iv : h ep - t h / 97 10 03 2 v 1 3 O ct 1 99 7 SMI - 25 - 97 Chaos in M ( atrix ) Theory

We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive feature of energy eigenvalues in quantum chaotic system. Chaotic dynamics in N = 2 supersymmetric Yang-Mills theory is also discussed. We demonstrate that after the separation of ”slow” and ”fast” modes there is a singular contribution from the ”slow” modes to the Hamiltonian of the ”fast” modes. Recent advances in string theory have led to the discovery of dualities between five known superstring theories. These theories are expected to be obtained by taking various limits of the conjectured eleven-dimensional M-theory [1, 2]. At low energies/large distances M-theory is described by eleven-dimensional supergravity. Banks, Fischler, Shenker and Susskind [3] have proposed that M-theory in the infinite momentum frame is described in terms of a supersymmetric matrix model, the so called M(artix) theory. Moreover, the only dynamical degrees of freedom are Dirichlet zero-branes and the calculation of any physical quantity of M-theory can be reduced to a calculation in the matrix quantum mechanics. A system of N Dirichlet zero-branes is described in terms of nine N × N Hermitian matrices Xi, i = 1, ..., 9 together with their fermionic superpartners. The action can be regarded as ten-dimensional SU(N) supersymmetric Yang-Mills theory dimensionally reduced to (0 + 1) space-time dimensions: