Non-abelian Born-Infeld and kappa-symmetry

We define an iterative procedure to obtain a non-abelian generalization of the Born-Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. In this paper we will present all bosonic terms in the action up to terms quartic in the Yang-Mills field strength and all fermion bilinear terms up to terms cubic in the field strength. Already at this order the fermionic terms do not satisfy the symmetric trace-prescription

M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory

A self-contained review is given of the matrix model of M-theory. The introductory part of the review is intended to be accessible to the general reader. M-theory is an eleven-dimensional quantum theory of gravity which is believed to underlie all superstring theories. This is the only candidate at present for a theory of fundamental physics which reconciles gravity and quantum field theory in a potentially realistic fashion. Evidence for the existence of M-theory is still only circumstantial---no complete background-independent formulation of the theory yet exists. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, the theory appeared in a different guise as the discrete light-cone quantization of M-theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory which reduces to a supersymmetric theory of gravity at low energies. Although the fundamental degrees of freedom of matrix theory are essentially pointlike, it is shown that higher-dimensional fluctuating objects (branes) arise through the nonabelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed.Comment: 56 pages, 3 figures, LaTeX, revtex style; v2: references adde