Supersymmetric (SUSY) Ward identities are considered for the N=1 SU(2) SUSY Yang Mills theory discretized on the lattice with Wilson fermions (gluinos). They are used in order to compute non-perturbatively a subtracted gluino mass and the mixing coefficient of the SUSY current. The computations were performed at gauge coupling β = 2.3 and hopping parameter κ = 0.1925, 0.194, 0.1955 using the two-step multi-bosonic dynamical-fermion algorithm. Our results are consistent with a scenario where the Ward identities are satisfied up to O(a) effects. The vanishing of the gluino mass occurs at a value of the hopping parameter which is not fully consistent with the estimate based on the chiral phase transition. This suggests that, although SUSY restoration appears to occur close to the continuum limit of the lattice theory, the results are still affected by significant systematic effects.

We present three-dimensional simulations of the dynamics of binary neutron star (BNS) mergers from the late stage of the inspiral process up to ∼ 20 ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH). We investigate five equalmass models of total gravitational mass 2.207, 2.373, 2.537, 2.697 and 2.854 M , respectively; and four unequal mass models with M ADM 2.53 M and q 0.94, 0.88, 0.83, and 0.77 (whereis the mass ratio). We use a semi-realistic equation of state (EOS), namely the seven-segment piece-wise polytropic SLyPP with a thermal component given by Γ th = 1.8. We have also compared the resulting dynamics (for one model) using both, the BSSN-NOK and CCZ4 methods for the evolution of the gravitational sector, and also different reconstruction methods for the matter sector, namely PPM, WENO and MP5. Our results show agreement and high resolution, but superiority of BSSN-NOK supplemented by WENO reconstruction at lower resolutions.One of the important characteristics of the present investigation is that for the first time, it has been done using only publicly available open source software: the Einstein Toolkit code, deployed for the dynamical evolution; and the LORENE code, for the generation of the initial models. All of the source code and parameters used for the simulations have been made publicly available. This not only makes it possible to re-run and re-analyze our data, but also enables others to directly build upon this work for future research.

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We study the high density region of QCD within an effective model obtained in the frame of the hopping parameter expansion and choosing Polyakov type of loops as the main dynamical variables representing the fermionic matter. To get a first idea of the phase structure, the model is analyzed in strong coupling expansion and using a mean field approximation. In numerical simulations, the model still shows the so-called sign problem, a difficulty peculiar to non-zero chemical potential, but it permits the development of algorithms which ensure a good overlap of the Monte Carlo ensemble with the true one. We review the main features of the model and present calculations concerning the dependence of various observables on the chemical potential and on the temperature, in particular of the charge density and the diquark susceptibility, which may be used to characterize the various phases expected at high baryonic density. We obtain in this way information about the phase structure of the model and the corresponding phase transitions and cross over regions, which can be considered as hints for the behaviour of non-zero density QCD.