Ferrara--Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D SYM
arXiv:1209.2473 · doi:10.1016/j.nuclphysb.2012.11.023
Abstract
It is well-known that Noether currents in the classical four-dimensional supersymmetric Yang--Mills theory (4D SYM), i.e., the current, the supersymmetry (SUSY) current and the energy-momentum tensor, form a multiplet under SUSY, called the Ferrara--Zumino supermultiplet. Inspired by this structure, we define the energy-momentum tensor in the lattice formulation of 4D SYM by a renormalized super transformation of a lattice SUSY current. By using a renormalized SUSY Ward--Takahashi relation, the energy-momentum tensor so constructed is shown to be conserved in the quantum continuum limit. Our construction of the energy-momentum tensor is very explicit and usable in non-perturbative numerical simulations.
27 pages, the final version to appear in Nucl. Phys. B
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