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 $δ_εΓ=0$ (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.