Fine-tunings and renormalization of gluino bilinear operators in lattice SYM with Stout-Smeared links

TL;DR

This work addresses renormalization in lattice $N=1$ supersymmetric Yang–Mills theory by performing a one-loop perturbative analysis with stout smeared links and Symanzik improved gluon actions. The authors compute gauge-variant two- and three-point Green functions in both dimensional and lattice regularizations to derive renormalization factors for the gluon and gluino fields, the gauge parameter, the coupling, and gluino bilinear operators $S$, $P$, and $A$ across three gluon actions and arbitrary parameters $c_{SW}$ and $\omega$. A key finding is that the axial current renormalization $Z_A$ can be preserved at one loop for suitable choices of the stout parameter and clover coefficient, and that the critical gluino mass $m_{\lambda}^{\rm crit.}$ can be driven to zero by appropriate parameter tuning, providing practical guidance for lattice SYM simulations. The results facilitate reliable continuum extrapolations and set the stage for future nonperturbative studies of SUSY on the lattice, including renormalization of gluino–glue operators and Noether supercurrent mixing.

Abstract

In this paper, we compute the renormalization factors for the gluino and gluon fields, the gauge parameter, the coupling constant, as well as the scalar, pseudoscalar, and axial-vector gluino bilinear operators in N=1 supersymmetric Yang-Mills (SYM) theory, using improved lattice actions. Our lattice formulation employs clover fermions, a Symanzik-improved gauge action, and stout-smeared links, which suppress ultraviolet fluctuations and thus enable more accurate determinations of renormalization factors. Our methodology involves computing gauge-variant two-point and three-point Green's functions at one-loop order in lattice perturbation theory, in order to extract the multiplicative renormalization factors and the critical gluino mass. By analyzing lattice discretization effects on the axial current and their dependence on the stout-smearing and clover parameters, we identify a value of the smearing parameter that ensures axial-current conservation at one loop. The results presented in this work provide practical guidance for the fine-tuning procedures required to set up and calibrate lattice simulations of SYM.

Figures (6)

• Figure 1: One-loop 1PI Feynman diagrams leading to the gluino self-energy on the lattice. A wavy (solid) line represents gluons (gluinos). Only the first diagram contributes in dimensional regularization.
• Figure 2: One-loop 1PI Feynman diagrams contributing to the gluon propagator at one-loop order. A wavy (solid, dotted) line represents gluons (gluinos, ghosts). The square vertex denotes contributions arising from measure term. The diagrams shown in the second row appear exclusively due to the lattice discretization and have no continuum counterparts.
• Figure 3: One-loop 1PI Feynman diagrams leading to the ghost propagator. A wavy (solid, dotted) line represents gluons (gluinos, ghosts). The second diagram appears only in the lattice regularization.
• Figure 4: One-loop 1PI Feynman diagrams contributing to the renormalization of the coupling constant. Wavy lines represent gluons, and dotted lines denote ghost fields. The second diagram in the first row and the diagrams in the second row contribute exclusively in the lattice regularization.
• Figure 5: One-loop Feynman diagram contributing to the two-point Green's functions of the gluino bilinear operators $\langle \lambda \, {\cal{O}}_\Gamma \, \bar{\lambda} \rangle$ . A wavy (solid) line represents gluons (gluinos). A cross denotes the insertion of ${\cal{O}}_\Gamma$.