4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

Kenji Hieda,Hiroki Makino,Hiroshi Suzuki,Aya Kasai,M Della Morte,E Gámiz Sánchez,C Pena Ruano,P Fritzsch

doi:10.1051/epjconf/201817511014

Abstract

The gradient flow [1–5] gives rise to a versatile method to construct renor-malized composite operators in a regularization-independent manner. By adopting this method, the authors of Refs. [6–9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D N = 1 super Yang–Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess–Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields [10].

Highlights

Lattice gauge theory provides a non-perturbative definition of quantum field theory (QFT) and a powerful tool of simulating it
These symmetries are often expected to be restored in the continuum limit, this fact complicates the construction of the Noether current associated with those spacetime symmetries, e.g. the energy-momentum tensor
In order to construct the composite operators in a regularizationindependent manner, we consider the gradient flow which is defined for the gauge field by

Summary

Introduction

Lattice gauge theory provides a non-perturbative definition of quantum field theory (QFT) and a powerful tool of simulating it. The first is a construction of the Noether current in a regularized theory; the second is to express it by flowed bare composite operators. Substituting these into Eq (17) and evaluating UV divergences coming from 1PI one-loop diagrams containing composite operators, after rearrangements of various terms, we have [10]. We can further show that the combination Xgf(x) + Xcc(x) vanishes in on-shell correlation functions of gauge-invariant operators [10] In such correlation functions, the correctly-normalized supercurrent to the one-loop level is given by

Supercurrent in terms of the flowed fields

Conclusion