Low-energy features of SU(2) Yang-Mills theory with light gluinos

We report on the latest results of the low-lying spectrum of bound states in SU(2) Yang-Mills theory with light gluinos. The behavior of the disconnected contributions in the critical region is analyzed. A first investigation of a three-gluino state is also discussed.Comment: Talk presented at LATTICE99(Higgs, Yukawa, SUSY), Pisa (Italy),3 pages; to be published in Nucl. Phys. B (Proc. Suppl.

Supermultiplets of the N=1 supersymmetric Yang-Mills theory in the continuum limit

The spectrum of N=1 supersymmetric Yang-Mills theory, calculated on the lattice, is presented. The masses have been determined on three different lattice spacings and extrapolated towards vanishing gluino mass. We present the extrapolation to the continuum limit which is consistent with the formation of degenerate supermultiplets.Comment: 7 pages, 4 figures; Proceedings of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japa

The light bound states of supersymmetric SU(2) Yang-Mills theory

Supersymmetry provides a well-established theoretical framework for extensions of the standard model of particle physics and the general understanding of quantum field theories. We summarise here our investigations of N=1 supersymmetric Yang-Mills theory with SU(2) gauge symmetry using the non-perturbative first-principles method of numerical lattice simulations. The strong interactions of gluons and their superpartners, the gluinos, lead to confinement, and a spectrum of bound states including glueballs, mesons, and gluino-glueballs emerges at low energies. For unbroken supersymmetry these particles have to be arranged in supermultiplets of equal masses. In lattice simulations supersymmetry can only be recovered in the continuum limit since it is explicitly broken by the discretisation. We present the first continuum extrapolation of the mass spectrum of supersymmetric Yang-Mills theory. The results are consistent with the formation of supermultiplets and the absence of non-perturbative sources of supersymmetry breaking. Our investigations also indicate that numerical lattice simulations can be applied to non-trivial supersymmetric theories.Comment: 19 pages, 6 figure

The low-lying spectrum of N=1 supersymmetric Yang-Mills theory

The spectrum of the lightest bound states in N=1 supersymmetric Yang-Mills theory with SU(2) gauge group, calculated on the lattice, is presented. The masses have first been extrapolated towards vanishing gluino mass and then to the continuum limit. The final picture is consistent with the formation of degenerate supermultiplets.Comment: 6 pages; 3 figures; proceedings of the EPS-HEP Conference 2015, 22-29 July 2015, Vienna, Austri

Influence of topology on the scale setting

Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t0 and w0 have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure in particular useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for N=1 supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster collaboration. For increasing flow time the topological charge quickly approaches near-integer values. The topological susceptibility has been measured for different fermion masses and its value is observed to approach zero in the chiral limit. Finally, the relation between the scale defined by the Wilson flow and the topological charge has been investigated, demonstrating a correlation between these two quantities.Comment: 17 pages, 12 figure

N=1 supersymmetric Yang-Mills theory on the lattice

Numerical simulations of supersymmetric theories on the lattice are intricate and challenging with respect to their theoretical foundations and algorithmic realisation. Nevertheless, the simulations of a four-dimensional supersymmetric gauge theory have made considerable improvements over the recent years. In this contribution we summarise the results of our collaboration concerning the mass spectrum of this theory. The investigation of systematic errors allows now a more precise estimate concerning the expected formation of supersymmetric multiplets of the lightest particles. These multiplets contain flavour singlet mesons, glueballs, and an additional fermionic state.Comment: presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Ward identities in N=1\mathcal{N}=1 supersymmetric SU(3) Yang-Mills theory on the lattice

The introduction of a space-time lattice as a regulator of field theories breaks symmetries associated with continuous space-time, i.e.\ Poincar{\'e} invariance and supersymmetry. A non-zero gluino mass in the supersymmetric Yang-Mills theory causes an additional soft breaking of supersymmetry. We employ the lattice form of SUSY Ward identities, imposing that their continuum form would be recovered when removing the lattice regulator, to obtain the critical hopping parameter where broken symmetries can be recovered.Comment: Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory at Granada, Spain (18-24 June 2017

Baryonic states in N=1\mathbf{\mathcal{N}=1} supersymmetric SU(2) Yang-Mills theory on the lattice

We extend our analysis of bound states in $\mathcal{N}=1$ supersymmetric Yang-Mills theory by the consideration of baryonic operators, which are composed of three gluino fields. The corresponding states are similar to the baryons in QCD, but due to the difference between gluino and quark fields, their properties and the fermion line contractions involved in their correlation functions are different from QCD. In this work, we first explain the derivation of these operators and the contractions needed in numerical calculations of their correlators. In contrast to QCD the correlators contain a spectacle piece, which requires methods for all-to-all propagators. We provide a first estimate of the two-point function and the mass of the lightest baryonic state in $\mathcal{N}=1$ supersymmetric Yang-Mills theory

Continuum extrapolation of Ward identities in N=1 supersymmetric SU(3) Yang-Mills theory

Ali S, Bergner G, Gerber H, et al. Continuum extrapolation of Ward identities in N=1 supersymmetric SU(3) Yang-Mills theory. EUROPEAN PHYSICAL JOURNAL C. 2020;80(6): 548.In N=1 supersymmetric Yang-Mills theory, regularised on a space-time lattice, in addition to the breaking by the gluino mass term, supersymmetry is broken explicitly by the lattice regulator. In addition to the parameter tuning in the theory, the supersymmetric Ward identities can be used as a tool to investigate lattice artefacts as well as to check whether supersymmetry can be recovered in the chiral and continuum limits. In this paper we present the numerical results of an analysis of the supersymmetric Ward identities for our available gauge ensembles at different values of the inverse gauge coupling beta and of the hopping parameter kappa. The results clearly indicate that the lattice artefacts vanish in the continuum limit, confirming the restoration of supersymmetry