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.

We determine the magnetic susceptibility of thermal QCD matter by means of first principles lattice simulations using staggered quarks with physical masses. A novel method is employed that only requires simulations at zero background field, thereby circumventing problems related to magnetic flux quantization. After a careful continuum limit extrapolation, diamagnetic behavior (negative susceptibility) is found at low temperatures and strong paramagnetism (positive susceptibility) at high temperatures. We revisit the decomposition of the magnetic susceptibility into spin-and orbital angular momentumrelated contributions. The spin term-related to the normalization of the photon lightcone distribution amplitude at zero temperature-is calculated non-perturbatively and extrapolated to the continuum limit. Having access to both the full magnetic susceptibility and the spin term, we calculate the orbital angular momentum contribution for the first time. The results reveal the opposite of what might be expected based on a free fermion picture. We provide a simple parametrization of the temperature-and magnetic field-dependence of the QCD equation of state that can be used in phenomenological studies.

Supersymmetry (SUSY) has been proposed to be a central concept for the physics beyond the standard model and for a description of the strong interactions in the context of the AdS/CFT correspondence. A deeper understanding of these developments requires the knowledge of the properties of supersymmetric models at finite temperatures. We present a Monte Carlo investigation of the finite temperature phase diagram of the N = 1 supersymmetric Yang-Mills theory (SYM) regularised on a space-time lattice. The model is in many aspects similar to QCD: quark confinement and fermion condensation occur in the low temperature regime of both theories. A comparison to QCD is therefore possible. The simulations show that for N = 1 SYM the deconfinement temperature has a mild dependence on the fermion mass. The analysis of the chiral condensate susceptibility supports the possibility that chiral symmetry is restored near the deconfinement phase transition.

We present the first lattice investigation of coupled-channel $$ D\overline{D} $$ D D ¯ and $$ {D}_s{\overline{D}}_s $$ D s D ¯ s scattering in the JPC = 0++ and 2++ channels. The scattering matrix for partial waves l = 0, 2 and isospin zero is determined using multiple volumes and inertial frames via Lüscher’s formalism. Lattice QCD ensembles from the CLS consortium with mπ ≃ 280 MeV, a ≃ 0.09 fm and L/a = 24, 32 are utilized. The resulting scattering matrix suggests the existence of three charmonium-like states with JPC = 0++ in the energy region ranging from slightly below 2mD up to 4.13 GeV. We find a so far unobserved $$ D\overline{D} $$ D D ¯ bound state just below threshold and a $$ D\overline{D} $$ D D ¯ resonance likely related to χc0(3860), which is believed to be χc0(2P). In addition, there is an indication for a narrow 0++ resonance just below the $$ {D}_s{\overline{D}}_s $$ D s D ¯ s threshold with a large coupling to $$ {D}_s{\overline{D}}_s $$ D s D ¯ s and a very small coupling to $$ D\overline{D} $$ D D ¯ . This resonance is possibly related to the narrow X(3915)/χc0(3930) observed in experiment also just below $$ {D}_s{\overline{D}}_s $$ D s D ¯ s . The partial wave l = 2 features a resonance likely related to χc2(3930). We work with several assumptions, such as the omission of J/ψω, ηcη and three-particle channels. Only statistical uncertainties are quantified, while the extrapolations to the physical quark-masses and the continuum limit are challenges for the future.

In numerical investigations of supersymmetric Yang-Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by the lattice discretisation. In this article we present an improved method for the numerical analysis of supersymmetric Ward identities, which takes into account the correlations between the various observables involved. We present the first complete analysis of supersymmetric Ward identities in N = 1 supersymmetric Yang-Mills theory with gauge group SU(3). The results indicate that lattice artefacts scale to zero as O(a 2 ) towards the continuum limit in agreement with theoretical expectations.