Witten index and phase diagram of compactified N=1 supersymmetric Yang-Mills theory on the lattice

Owing to confinement, the fundamental particles of N=1 Supersymmetric Yang-Mills (SYM) theory, gluons and gluinos, appear only in colourless bound states at zero temperature. Compactifying the Euclidean time dimension with periodic boundary conditions for fermions preserves supersymmetry, and confinement is predicted to persist independently of the length of the compactified dimension. This scenario can be tested non-perturbatively with Monte-Carlo simulations on a lattice. SUSY is, however, broken on the lattice and can be recovered only in the continuum limit. The partition function of compactified N=1 SYM theory with periodic fermion boundary conditions corresponds to the Witten index. Therefore it can be used to test whether supersymmetry is realized on the lattice. Results of our recent numerical simulations are presented, supporting the disappearance of the deconfinement transition in the supersymmetric limit and the restoration of SUSY at low energies.Comment: 7 pages, 3 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japa

Phase structure of the N=1 supersymmetric Yang-Mills theory at finite temperature

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.Comment: 26 pages, 12 figure

EFFECTS OF EVIDENCE-BASED DISCHARGE INSTRUCTIONS ON FOLLOW-UP WITH A HEALTHCARE PROVIDER IN PATIENTS PRESENTING WITH MTBI-LIKE SYMPTOMS TO A HEALTH CLINIC AT A RURAL SPORTS CAMP IN THE PACIFIC NORTHWEST IN THE U.S.

Mild traumatic brain injury (mTBI) is a major public health burden affecting both children and adults in the U. S. (Sarmiento et al., 2019; Schuchat, Houry, & Baldwin, 2018). The management of mTBI at summer camps is not well characterized in the literature. Epidemiologic studies on summer camps have reported that 25% of all injuries were to the head, face and/or neck (Kolberg et al., 2020; Robinson, Arbogast, Garst & Corwin 2019). The purpose of this project was to evaluate the impact of evidence-based instructions for follow-up with a healthcare provider in patients presenting with mTBI-like symptoms to a health clinic at a rural summer sports camp. The number of symptoms over time and risk factors for protracted recovery were explored in this small, prospective, observational project. Most of the patients (82%, n = 6) followed-up within 2 weeks of injury with primary care (43%, n = 6) or the camp nurse (36%, n = 5). The total number of symptoms decreased over time, but those with ≥ 3 risk factors reported a greater median number of symptoms after 2 weeks. Three patients (27%) reported persistent symptoms after 4 weeks. Adapting mTBI guidelines to the summer camp setting, using available evidence-based resources for anticipatory guidance and follow-up recommendations would be beneficial (Lumba-Brown et al., 2018a; McCrory et al., 2017)

Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition

Fermion boundary conditions play a relevant role in revealing the confinement mechanism of N=1 supersymmetric Yang-Mills theory with one compactified space-time dimension. A deconfinement phase transition occurs for a sufficiently small compactification radius, equivalent to a high temperature in the thermal theory where antiperiodic fermion boundary conditions are applied. Periodic fermion boundary conditions, on the other hand, are related to the Witten index and confinement is expected to persist independently of the length of the compactified dimension. We study this aspect with lattice Monte Carlo simulations for different values of the fermion mass parameter that breaks supersymmetry softly. We find a deconfined region that shrinks when the fermion mass is lowered. Deconfinement takes place between two confined regions at large and small compactification radii, that would correspond to low and high temperatures in the thermal theory. At the smallest fermion masses we find no indication of a deconfinement transition. These results are a first signal for the predicted continuity in the compactification of supersymmetric Yang-Mills theory.Comment: 17 pages, 9 Figure

Analysis of shear test method for composite laminates

An elastic plane stress finite element analysis of the stress distributions in four flat test specimens for in-plane shear response of composite materials subjected to mechanical or thermal loads is presented. The shear test specimens investigated include: slotted coupon, cross beam, losipescu, and rail shear. Results are presented in the form of normalized shear contour plots for all three in-plane stess components. It is shown that the cross beam, losipescu, and rail shear specimens have stress distributions which are more than adequate for determining linear shear behavior of composite materials. Laminate properties, core effects, and fixture configurations are among the factors which were found to influence the stress distributions

Color confinement and random matrices. A random walk down group manifold toward Casimir scaling

Abstract We explain the microscopic origin of linear confinement potential with the Casimir scaling in generic confining gauge theories. In the low-temperature regime of confining gauge theories such as QCD, Polyakov lines are slowly varying Haar random modulo exponentially small corrections with respect to the inverse temperature, as shown by one of the authors (M. H.) and Watanabe. With exact Haar randomness, computation of the two-point correlator of Polyakov loops reduces to the problem of random walk on group manifold. Linear confinement potential with approximate Casimir scaling except at short distances follows naturally from slowly varying Haar randomness. With exponentially small corrections to Haar randomness, string breaking and loss of Casimir scaling at long distance follow. Hence we obtain the Casimir scaling which is only approximate and holds only at intermediate distance, which is precisely needed to explain the results of lattice simulations. For (1 + 1)-dimensional theories, there is a simplification that admits the Casimir scaling at short distances as well

Flow Equation for Supersymmetric Quantum Mechanics

We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic super-covariant derivative expansion and concentrate on systems with unbroken supersymmetry. Already at next-to-leading order, the energy of the first excited state for convex potentials is accurately determined within a 1% error for a wide range of couplings including deeply nonperturbative regimes.Comment: 24 pages, 8 figures, references added, typos correcte