On the Supersymmetry and Gauge Structure of Matrix Theory

TL;DR

This paper derives the supersymmetric Ward identity for Matrix Theory's effective action, revealing how quantum corrections influence supersymmetry transformations and confirming that supersymmetry constrains the action's form at one-loop order.

Contribution

It provides a formalism to directly identify quantum-corrected supersymmetry transformations for supergravitons in Matrix Theory, demonstrating their interplay with gauge symmetry.

Findings

Supersymmetric Ward identity derived for arbitrary supergraviton trajectories.

Quantum-corrected supersymmetry transformations explicitly computed at 1-loop.

Supersymmetry uniquely determines the effective action's form at lowest order.

Abstract

Supersymmetric Ward identity for the low energy effective action in the standard background gauge is derived for {\it arbitrary} trajectories of supergravitons in Matrix Theory. In our formalism, the quantum-corrected supersymmetry transformation laws of the supergravitons are directly identified in closed form, which exhibit an intricate interplay between supersymmetry and gauge (BRST) symmetry. As an application, we explicitly compute the transformation laws for the source-probe configuration at 1-loop and confirm that supersymmetry fixes the form of the action completely, including the normalization, to the lowest order in the derivative expansion.