Perturbative renormalization of the supercurrent operator in lattice $\mathcal{N}=1$ supersymmetric Yang-Mills theory

Abstract

In this work we perform a perturbative study of the Noether supercurrent operator in the context of Supersymmetric $\mathcal{N}=1$ Yang-Mills (SYM) 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 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 $\overline{MS}$-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 $\overline{MS}$ 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.

17 pages, 3 figures, 1 table

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• Supersymmetric QCD on the Lattice: An Exploratory Study
• Numerical results for the lightest bound states in $\mathcal{N}=1$ supersymmetric SU(3) Yang-Mills theory
• Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor
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Cited by in corpus (2)

• Lattice studies of supersymmetric gauge theories
• Nonperturbative renormalization of the supercurrent in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory