Noether supercurrent operator mixing from lattice perturbation theory

TL;DR

This paper computes the one-loop perturbative renormalization and operator mixing of the supercurrent in lattice ${ m N}=1$ Supersymmetric Yang-Mills theory, addressing operator mixing complexities on the lattice.

Contribution

It provides the first two rows of the supercurrent mixing matrix in lattice perturbation theory, including the renormalization of the supercurrent and gauge invariant mixing operator.

Findings

Determined mixing coefficients for supercurrent and related operators.

Performed calculations in both dimensional and lattice regularizations.

Used Wilson fermions with clover improvement on the lattice.

Abstract

In this work we present perturbative results for the renormalization of the supercurrent operator, $S_\mu$, in ${\cal N} =1$ Supersymmetric Yang-Mills theory. At the quantum level, this operator mixes with both gauge invariant and noninvariant operators, which have the same global transformation properties. In total, there are 13 linearly independent mixing operators of the same and lower dimensionality. We determine, via lattice perturbation theory, the first two rows of the mixing matrix, which refer to the renormalization of $S_\mu$, and of the gauge invariant mixing operator, $T_\mu$. To extract these mixing coefficients in the ${\overline{\rm MS}}$ renormalization scheme and at one-loop order, we compute the relevant two-point and three-point Green's functions of $S_\mu$ and $T_\mu$ in two regularizations: dimensional and lattice. On the lattice, we employ the plaquette gluonic action and for the gluinos we use the fermionic Wilson action with clover improvement.