Towards a complete description of multiple D$p$-brane systems: Multiple D$0$ Story

TL;DR

This thesis develops a fully nonlinear, doubly supersymmetric action for nearly coincident multiple D0-branes, advancing the geometric and quantization understanding of such systems in string theory.

Contribution

It introduces a new supersymmetric action for multiple D0-branes and initiates a quantization program for a novel supersymmetric field theory.

Findings

Constructed a nonlinear, doubly supersymmetric action for multiple D0-branes.

Developed a geometric framework using the spinor moving frame formalism.

Laid groundwork for a supersymmetric field theory with matrix coordinates.

Abstract

In this thesis, we address the problem of constructing the complete supersymmetric description of systems of $N$ nearly coincident Dirichlet $p$-branes (multiple D$p$-brane or mD$p$). A particularly important result is a completely nonlinear action for the 10-dimensional dynamical system of nearly coincident multiple D$0$-branes (mD$0$) which is doubly supersymmetric, i.e. it is invariant under both spacetime (target superspace) supersymmetry and the worldline supersymmetry; the latter is a counterpart of the local fermionic $\kappa$-symmetry characteristic of a single D$0$-brane (Dirichlet superparticle). This problem is approached in flat superspace using the (spinor) moving frame formalism, which provides us with a geometric framework to the treatment of supersymmetric particles and extended objects ($p$-branes) in higher dimensions. Furthermore, we have initiated the quantization program aimed at development of a field theory of multiple D$0$-branes. This quantization in its complete form is expected to lead to a novel supersymmetric field theory formulated on a superspace extended by additional bosonic and fermionic matrix coordinates, whose development may offer significant insights into the deeper structure of String/M-theory.