Power of supersymmetry in D-particle dynamics

Abstract

A new systematic method is developed to study to what extent the symmetry requirements alone, above all the invariance under 16 supersymmetries (SUSY), determine the completely off-shell effective action Γ of a D-particle, i.e., without imposing any restrictions on its position r m ( τ) and spin θ α ( τ). Our method consists of (i) writing down the proper closure relations for general SUSY transformations δ ϵ (which necessarily involves Γ itself) together with the invariance condition δ ϵ Γ=0 (ii) and solving this coupled system of functional differential equations for δ ϵ and Γ simultaneously, modulo field redefinitions, in a consistent derivative expansion scheme. Our analysis is facilitated by a novel classification scheme introduced for the terms in Γ. At order 2 and 4, although no assumption is made on the underlying theory, we reproduce the effective action previously obtained at the tree and the 1-loop level in Matrix theory respectively (modulo two constants), together with the quantum-corrected SUSY transformations which close properly. This constitutes a complete unambiguous proof of off-shell non-renormalization theorems.