Zero and One-dimensional Probes with N=8 Supersymmetry

TL;DR

This paper analyzes the symmetry structure of N=8 quantum mechanics related to D0-brane probes in type I' string theory, resolving supersymmetry puzzles and exploring implications for string theory and M theory.

Contribution

It clarifies how supersymmetry is preserved in N=8 quantum mechanics with gauge constraints and central charges, providing insights into D0-brane dynamics and matrix models.

Findings

Supersymmetry is preserved despite boson-fermion imbalance.

Zero-point energy results in a linear potential consistent with supersymmetry.

The metric remains largely unconstrained by the analysis.

Abstract

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.