A Non-Renormalization Theorem for the d=1, N=8 Vector Multiplet

TL;DR

This paper proves a non-renormalization theorem for d=1, N=8 vector multiplet sigma models, showing their metric is uniquely determined and remains unchanged by quantum corrections under certain symmetry conditions.

Contribution

It introduces a manifestly d=1, N=4 super-space formalism for analyzing N=8 supersymmetric sigma models and establishes a non-renormalization theorem for their metrics.

Findings

The sigma model metric is uniquely determined by one-loop results.

The metric is not renormalized perturbatively or non-perturbatively.

The formalism applies to various D-brane configurations.

Abstract

Sigma models describing low energy effective actions on D0-brane probes with N=8 supercharges are studied in detail using a manifestly d=1, N=4 super-space formalism. Two 0+1 dimensional N=4 multiplets together with their general actions are constructed. We derive the condition for these actions to be N=8 supersymmetric and apply these techniques to various D-brane configurations. We find that if in addition to N=8 supersymmetry the action must also have Spin(5) invariance, the form of the sigma model metric is uniquely determined by the one-loop result and is not renormalized perturbatively or non-perturbatively.