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° twist effectively removes 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° 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 DDαAMG multigrid algorithm accelerates the inversion of the Wilson Dirac operator considerably. On a 163× 32 lattice, speed-up factors of up to 20 are reached if commonly used algorithms are replaced by the DDαAMG.
Highlights
Where every bosonic particle has a fermionic superpartner with the same quantum numbers and vice versa
In this article we investigate the properties of 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 Quantum Chromodynamics (QCD)
In this work we have introduced, analyzed and applied a new type of Wilson Dirac operator for lattice calculations of N = 1 supersymmetric SU(3) Yang-Mills theory
Summary
The action in eq (2.1) contains a finite gluino mass m which breaks supersymmetry softly On the lattice this mass is fine-tuned such that after continuum extrapolation a supersymmetric limit is reached which at the same time is chirally symmetric. Supersymmetry and chiral symmetry are broken simultaneously by the discretization and Wilson term This breaking leads to a relevant counter-term, which is proportional to the gluino mass term. Since the gluino mass term is the only relevant operator, supersymmetry and chiral symmetry will be restored in the continuum limit. By fine-tuning to the critical gluino mass mcrit we are able to recover in the continuum limit simultaneously supersymmetry as well as chiral symmetry. Since the Pfaffian is proportional to the square root of the determinant, the rational hybrid Monte Carlo algorithm (RHMC) [46] is used in our simulations
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