Fully Off-shell Effective Action and its Supersymmetry in Matrix Theory II

TL;DR

This paper proves that the fully off-shell effective action in Matrix theory is uniquely determined by supersymmetry constraints at one loop, implying potential all-order uniqueness in perturbation theory.

Contribution

It demonstrates that the SUSY Ward identity uniquely determines the effective action from the supersymmetry transformation without explicit calculations.

Findings

SUSY Ward identity constrains the effective action uniquely.

The approach suggests all-order uniqueness in perturbation theory.

No explicit form of quantum-corrected SUSY transformation needed.

Abstract

In a previous work, we computed the fully off-shell effective action $\Gamma$ and the corresponding quantum-corrected supersymmetry (SUSY) transformation operator $\delta_\epsilon$ for the so-called source-probe configuration in Matrix theory at one loop at order 4 in the derivative expansion, and showed that they satisfy the SUSY Ward identity $\delta_\epsilon \Gamma=0$. In this article, starting from the most general form of $\Gamma$, we demonstrate that, conversely, given such $\delta_\epsilon$ the SUSY Ward identity determines $\Gamma$ uniquely to the order specified above. Our demonstration does not require the explicit knowledge of the quantum-corrected supersymmetry transformation and hence strongly suggests that the uniqueness property would persist to all orders in perturbation theory.