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

TL;DR

This paper calculates the complete one-loop effective action for a probe D-particle in Matrix theory, including spin effects, and verifies its supersymmetry invariance, providing predictions for supergravity.

Contribution

It provides the first full off-shell effective action including spin effects and explicitly derives the quantum-corrected supersymmetry transformations in Matrix theory.

Findings

Effective action verified to be supersymmetry invariant.

Derived explicit supersymmetry transformation laws.

Predicted supergravity results based on Matrix theory calculations.

Abstract

As a step toward clarification of the power of supersymmetry (SUSY) in Matrix theory, a complete calculation, including all the spin effects, is performed of the effective action of a probe D-particle, moving along an arbitrary trajectory in interaction with a large number of coincident source D-particles, at one loop at order 4 in the derivative expansion. Furthermore, exploiting the SUSY Ward identity developed previously, the quantum-corrected effective supersymmetry transformation laws are obtained explicitly to the relevant order and are used to verify the SUSY-invariance of the effective action. Assuming that the agreement with 11-dimensional supergravity persists, our result can be regarded as a prediction for supergravity calculation, which, yet unavailable, is known to be highly non-trivial.