$\mathcal{N}=1$ Super-Yang-Mills theory on the lattice with twisted mass fermions

TL;DR

This paper explores a lattice formulation of $ =1$ Super-Yang-Mills theory using twisted mass fermions, demonstrating improved supersymmetry restoration and reduced discretization errors at finite lattice spacing, along with computational acceleration techniques.

Contribution

It introduces a twisted mass approach in lattice SYM that enhances supersymmetry and reduces discretization errors, improving continuum extrapolation and computational efficiency.

Findings

Twisted mass effectively reduces mass splitting of superpartners.

Discretization errors of order $ ext{O}(a)$ are suppressed at 45° twist.

DD$oldsymbol{ ext{α}}$AMG algorithm accelerates Dirac operator inversion by up to 20 times.

Abstract

Super-Yang-Mills theory (SYM) is a central building block for supersymmetric extensions of the Standard Model of particle physics. Whereas the weakly coupled subsector of the latter can be treated within a perturbative setting, the strongly coupled subsector must be dealt with a non-perturbative approach. Such an approach is provided by the lattice formulation. Unfortunately a lattice regularization breaks supersymmetry and consequently the mass degeneracy within a supermultiplet. In this article we investigate the properties of $\mathcal{N}=1$ supersymmetric SU(3) Yang-Mills theory with a lattice Wilson Dirac operator with an additional parity mass, similar as in twisted mass lattice QCD. We show that a special $45^\circ$ twist effectively moves the mass splitting of the chiral partners. Thus, at finite lattice spacing both chiral and supersymmetry are enhanced resulting in an improved continuum extrapolation. Furthermore, we show that for the non-interacting theory at $45^\circ$ twist discretization errors of order $\mathcal{O}(a)$ are suppressed, suggesting that the same happens for the interacting theory as well. As an aside, we demonstrate that the DD$\alpha$AMG multigrid algorithm accelerates the inversion of the Wilson Dirac operator considerably. On a $16^3\times 32$ lattice, speed-up factors of up to 20 are reached if commonly used algorithms are replaced by the DD$\alpha$AMG.