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In the present work we analyse N = (2, 2) supersymmetric Yang-Mills (SYM) theory with gauge group SU (2) in two dimensions by means of lattice simulations. The theory arises as dimensional reduction of N = 1 SYM theory in four dimensions. As in other gauge theories with extended supersymmetry, the classical scalar potential has flat directions which may destabilize numerical simulations. In addition, the fermion determinant need not be positive and this sign-problem may cause further problems in a stochastic treatment. We demonstrate that N = (2, 2) super Yang-Mills theory has actually no sign problem and that the flat directions are lifted and thus stabilized by quantum corrections. Only the bare mass of the scalars experience a finite additive renormalization in this finite theory. On various lattices with different lattice constants we determine the scalar masses and hopping parameters for which the supersymmetry violating terms are minimal. By studying four Ward identities and by monitoring the π-mass we show that supersymmetry is indeed restored in the continuum limit. In the second part we calculate the masses of the low-lying bound states. We find that in the infinite-volume and supersymmetric continuum limit the Veneziano-Yankielowicz super-multiplet becomes massless and the Farrar-Gabadadze-Schwetz super-multiplet decouples from the theory. In addition, we estimate the masses of the excited mesons in the Veneziano-Yankielowicz multiplet. We observe that the gluino-glueballs have comparable masses to the excited mesons.

Abstract. Supersymmetric gauge theories are an important building block for extensions of the standard model. As a first step towards Super-QCD we investigate the pure gauge sector with gluons and gluinos on the lattice, in particular the low energy mass spectrum: meson-like gluinoballs, gluino-glueballs and pure glueballs. We report on some first calculations performed with clover improved Wilson fermions on rather small lattices. The supersymmetric continuum limit and particle masses are discussed and compared to predictions from effective field theory.

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 $$ \mathcal{N} $$ 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 $$ \mathcal{O}(a) $$ 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.