A Theorem on the Power of Supersymmetry in Matrix Theory

TL;DR

This paper proves that, in Matrix theory with supersymmetry, the effective action is uniquely determined by SUSY Ward identities at all orders, assuming SO(9) symmetry is maintained, without needing detailed quantum correction data.

Contribution

It establishes a general theorem showing the uniqueness of the off-shell effective action in Matrix theory based solely on SUSY and symmetry considerations.

Findings

Effective action is uniquely fixed by SUSY Ward identities.

Proof relies only on tree-level SUSY transformations, not quantum corrections.

The result holds to all orders in perturbation theory, assuming SO(9) symmetry is preserved.

Abstract

For the so-called source-probe configuration in Matrix theory, we prove the following theorem concerning the power of supersymmetry (SUSY): Let $\delta$ be a quantum-corrected effective SUSY transformation operator expandable in powers of the coupling constant $g$ as $\delta = \sum_{n\ge 0} g^{2n} \delta^{(n)}$, where $\delta^{(0)}$ is of the tree-level form. Then, apart from an overall constant, the SUSY Ward identity $\delta \Gamma=0$ determines the off-shell effective action $\Gamma$ uniquely to arbitrary order of perturbation theory, provided that the $ SO(9)$ symmetry is preserved. Our proof depends only on the properties of the tree-level SUSY transformation laws and does not require the detailed knowledge of quantum corrections.