Zero and One-dimensional Probes with N=8 Supersymmetry

We study the symmetry structure of N=8 quantum mechanics, and apply it to the physics of D0-brane probes in type I' string theory. We focus on the theory with a global $Spin(8)$ R symmetry which arises upon dimensional reduction from $2d$ field theory with $(0,8)$ supersymmetry. There are several puzzles involving supersymmetry which we resolve. In particular, by taking into account the gauge constraint and central charge we explain how the system preserves supersymmetry despite having different numbers of bosonic and fermionic variables. The resulting zero-point energy leads to a linear potential consistent with supersymmetry, and the metric is largely unconstrained. We discuss implications for type I' string theory and the matrix model proposal for M theory.

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