Perturbative renormalization of the supercurrent operator in lattice supersymmetric Yang-Mills theory
G. Bergner (University of Jena, Institute for Theoretical Physics, Max-Wien-Platz 1, D-07743 Jena, Germany); M. Costa (Department of Physics, University of Cyprus, 1 Panepistimiou Avenue, 2109 Aglantzia, Nicosia, Cyprus); H. Panagopoulos (Department of Physics, University of Cyprus, 1 Panepistimiou Avenue, 2109 Aglantzia, Nicosia, Cyprus); I. Soler (University of Jena, Institute for Theoretical Physics, Max-Wien-Platz 1, D-07743 Jena, Germany); G. Spanoudes (Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus)
In this work we perform a perturbative study of the Noether supercurrent operator in the context of supersymmetric Yang-Mills theory on the lattice. The supercurrent mixes with several other operators, some of which are not gauge invariant, having the same quantum numbers. We determine, to one-loop order, the renormalization and all corresponding mixing coefficients by computing the relevant Green’s functions of each one of the mixing operators with external elementary fields. Our calculations are performed both in dimensional and lattice regularization. From the first regularization we obtain the -renormalized Green’s functions; comparison of the latter with the corresponding Green’s functions in the lattice regularization leads to the extraction of the lattice renormalization factors and mixing coefficients in the scheme. The lattice calculations are performed to lowest order in the lattice spacing, using Wilson gluons and clover improved gluinos. The lattice results can be used in nonperturbative studies of supersymmetric Ward identities.
