Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-10-15
Nucl.Phys.B656:93-131,2003
Physics
High Energy Physics
High Energy Physics - Theory
44 pages, v2: typos corrected, published version
Scientific paper
10.1016/S0550-3213(03)00115-9
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 $\Gamma$ of a D-particle, i.e. without imposing any restrictions on its position $r^m(\tau)$ and spin $\theta_\alpha(\tau)$. Our method consists of (i) writing down the proper closure relations for general SUSY transformations $\delta_\epsilon$ (which necessarily involves $\Gamma$ itself) together with the invariance condition $\delta_\epsilon\Gamma=0$ (ii) and solving this coupled system of functional differential equations for $\delta_\epsilon$ and $\Gamma$ simultaneously, modulo field redefinitions, in a consistent derivative expansion scheme. Our analysis is facilitated by a novel classification scheme introduced for the terms in $\Gamma$. 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.
Kazama Yoichi
Muramatsu Takaki
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