Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent

TL;DR

This paper extends a gradient flow-based method for defining a supercurrent from 4D $ abla=1$ to 4D $ abla=2$ super Yang--Mills theory, aiding future lattice simulations of supersymmetric models.

Contribution

It introduces a regularization-independent supercurrent construction for 4D $ abla=2$ SYM using gradient flow, building on previous work for $ abla=1$ theories.

Findings

Supercurrent expressed in a regularization-independent manner.

Facilitates fine tuning in lattice simulations of $ abla=2$ SYM.

Provides a foundation for supersymmetric continuum limit studies.

Abstract

In K.~Hieda, A.~Kasai, H.~Makino, and H.~Suzuki, Prog.\ Theor.\ Exp.\ Phys.\ \textbf{2017}, 063B03 (2017), a properly normalized supercurrent in the four-dimensional (4D) $\mathcal{N}=1$ super Yang--Mills theory (SYM) that works within on-mass-shell correlation functions of gauge-invariant operators is expressed in a regularization-independent manner by employing the gradient flow. In the present paper, this construction is extended to the supercurrent in the 4D $\mathcal{N}=2$ SYM. The so-constructed supercurrent will be useful, for instance, for fine tuning of lattice parameters toward the supersymmetric continuum limit in future lattice simulations of the 4D $\mathcal{N}=2$ SYM.