U Sp(2k) Matrix Model * )

We review the construction and theoretical implications of the USp(2k) matrix model in zero dimension introduced in ref. 1), . It is argued that the model provides a constructive approach to TypeI superstrings and is at the same time dynamical theory of spacetime points. Three subjects are discussed : semiclassical pictures and series of degenerate perturbative vacua associated with the worldvolume representation of the model, the formation of extended (D−) objects from the fermionic integrations via the (non-)abelian Berry phase, and the Schwinger-Dyson/loop equations which exhibit the joining-splitting interactions required. ∗) based on the lecture given by the first author at the 13th Nishinomiya-Yukawa Memorial Symposium “Dynamics of Fields and Strings” (November 12-13,1998) and on the lecture by the second author at the YITP workshop (November 16-18, 1998). ∗∗) [email protected] ∗∗∗) [email protected] 1 typeset using PTPTEX.sty §