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Chapter 4 Oscillating D-Strings from IIB Matrix Theory

One of the most challenging problem in string theory has been to understand its strong coupling aspects[l, 2], including its moduli space structure in full quantum theory at the nonperturbative level. One also hopes that such an investigation will lead to an understanding of supersymmetry breaking in these theories and will give the correct string theory vacuum describing the real world. As is well known, the unravelling of non-perturbative aspects includes an analysis of its soliton spectrum[3], and their moduli dependence. Investigations along these lines have also led to a better understanding of the confinement mechanism in supersymmetric gauge theories from string theory point of view[4]. A useful mechanism in studying the strong coupling aspects has been the D-brane con­ structions of sting solitons[5]. As a result, one can obtain the soliton spectrum and their interactions using open string Conformal Field Theory. Since the D-branes preserve a cer­ tain amount of supersymmetry, these are stable solitonic superstring vacua, around which a quantum field theory of the world-volume degrees of freedom can be formulated [6]. Many such D-brane configurations have been obtained [7] and the corresponding effective worldvolume action have been analyzed. Among these, of particular interest have been some of the six[8] and two[9] dimensional supersymmetric gauge theories. In the Matrix Theory[10][6, 11, 12] proposal by Banks, Fischler, Shenker and Susskind (BFSS), the SU(N) (N oo) world-volume gauge theory of N D-branes have themselves been conjectured to be a fundamental theory describing both the perturbative and nonperturbative aspects of string theory. In simplest cases, these are the dimensional reduction