arXiv:hep-th/0108233v1 31 Aug 2001 D0-branes with non-zero angular momentum George K. Savvidy National Research Center Demokritos, Ag. Paraskevi, GR-15310 Athens, Hellenic Republic Abstract. In my talk I shall consider the mechanism of self-expansion of a system of N D0-branes into high- dimensional non-commutative world-volume investigated by Harmark and Savvidy in [1]. Here D2- brane is formed due to the internal angular momentum of D0-brane system. The idea is that attractive force of tension should be cancelled by the centrifugal motion preventing a D-brane system from collapse to a lower-dimensional one. I shall also present a new extended solution where a total of 9 space dimensions is used to embed a D0-brane system. In the last section, by performing linear analysis, the stability of the system is demonstrated. INTRODUCTION In the last years there has been increasing interest in dimensionally reduced supersym- metric Yang-Mills theories [2, 3, 4]. One of the reasons is that the reduction of ten- dimensional theory to p + 1 dimension is relevant for the description of Dp-branes, p- dimensional extended objects carrying Ramond-Ramond (RR) charges in type II super- string theories [5]. In the extreme reduction to zero dimensions it is believed to describe D0-branes, fundamental pointlike objects in type IIA superstring theory [6]. In certain energy regimes the dynamics of N such particles can be described by the supersymmetric quantum mechanics of N × N Hermitian matrices obtained from dimensional reduction of N = 1, D = 10 super-Yang-Mills theory down to 0 + 1 dimensions 1 . It is believed that supersymmetric quantum mechanics of many D0-branes in type IIA superstring theory is equivalent to a partonic description of light-front M-theory [11], a more fundamental underlying M-theory [8, 9, 10]. The existence of matrix formulation of M-theory [11], the BRSS-conjecture, crucially relies on the existence within type-IIA string theory of a tower of massive BPS particles electrically charged with respect to the RR 1-form. These particles originally described as black holes in IIA supergravity were identified with D0-branes and can be interpreted as Kaluza-Klein particles of eleven-dimensional M-theory compactified on a circle. The existence of the M-theoretic Kaluza-Klein tower of states is equivalent to the statement that supersymmetric Yang- Mills quantum mechanics has exactly one bound state for each N [12, 13, 14]. Remarkable aspect of matrix theory is that not only classical gravitational interactions can be produced in the large N-limit, but also the appearance of the superstring extended objects in terms of pointlike fundamental degrees of freedom. One example of such 1 It was also proposed that 0 + 0- dimensional matrix model should give a Poincare invariant non- perturbative definition of IIB superstring theory, the so-called IKKT model [7].