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

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

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

Bubble formation in ϕ6\phi^6 potential

Scalar field theory with an asymmetric potential is studied at zero temperature and high-temperature for $\phi^6$ potential. The equations of motion are solved numerically to obtain O(4) spherical symmetric and O(3) cylindrical symmetric bounce solutions. These solutions control the rates for tunneling from the false vacuum to the true vacuum by bubble formation. The range of validity of the thin-wall approximation (TWA) is investigated. An analytical solution for the bounce is presented, which reproduces the action in the thin-wall as well as the thick-wall limits.Comment: 22 pag

EmoCycling – Analysen von Radwegen mittels Humansensorik und Wearable Computing

Radfahren erfreut sich einer zunehmenden Wertschätzung. Einerseits als neuer Lifestyle, andererseits als wichtiges Thema der städtischen Mobilitätsplanung: Bike-Sharing-Angebote, Radwegekonzepte und Förderung eines umweltfreundlichen Mobilitätsmix sind hierbei wichtige Stichworte. Daher fördern zunehmend mehr Städte den Ausbau der Radwege-Infrastruktur, um das Radfahren attraktiver zu gestalten. Wie stark Radfahren aber tatsächlich angenommen und praktiziert wird, hängt von ganz verschiedenen Faktoren ab: Verkehrslage, Quantität und Qualität der Infrastruktur, Topografie sowie das subjektive Sicherheitsempfinden z.B. an unübersichtlichen Kreuzungen beeinflussen die Verkehrsmittelwahl. Insbesondere die Erfassung und Analyse des subjektiven Sicherheitsempfindens stellt hierbei eine große Herausforderung dar – wird aber durch neue Methoden der Humansensorik (Exner et al. 2012) möglich. Entwicklungen in den Bereichen des Wearable Computing sowie der Geoinformatik ermöglichen es, das subjektive Sicherheitsempfinden während der Fahrt genauer zu analysieren. Anknüpfend an Projekte zur emotionalen Stadtkartierung (Höffken et al. 2008, Zeile et al. 2010) erfolgt ein Live-Monitoring der Probanden während der Fahrt. Mittels eines Sensorarmbands (Smartband) zur Erfassung psychophysiologischer Reaktionen des Körpers in Kombination mit Video-Kamera-Daten und GPS-Koordinaten wird der emotionale Zustand der Probanden sekundengenau gemessen. Dadurch lassen sich Emotionen, insbesondere Stress, interpretieren und auf einer Karte verorten sowie die Auslöser (Trigger) identifizieren. Zudem kann auf diese Weise der Verkehr kontinuierlich erfasst und in die Analyse mit aufgenommen werden, um Gefahrenstellen zu lokalisieren. Nach einer Einführung in das Thema Radfahren in der Untersuchungsgemeinde Kaiserslautern, gibt das Paper einen Überblick über den aktuellen Stand der Methodik, die Konzeptionierung der Teststrecken sowie die Methodik im konkreten Projekt EmoCycling. Darauf basierend werden die Ergebnisse des Projektes vorgestellt und daraus resultierende weiterführende Fragenstellungen aufgezeigt

Spectral pattern similarity analysis: Tutorial and application in developmental cognitive neuroscience

The human brain encodes information in neural activation patterns. While standard approaches to analyzing neural data focus on brain (de-)activation (e.g., regarding the location, timing, or magnitude of neural responses), multivariate neural pattern similarity analyses target the informational content represented by neural activity. In adults, a number of representational properties have been identified that are linked to cognitive performance, in particular the stability, distinctiveness, and specificity of neural patterns. However, although growing cognitive abilities across childhood suggest advancements in representational quality, developmental studies still rarely utilize information-based pattern similarity approaches, especially in electroencephalography (EEG) research. Here, we provide a comprehensive methodological introduction and step-by-step tutorial for pattern similarity analysis of spectral (frequency-resolved) EEG data including a publicly available pipeline and sample dataset with data from children and adults. We discuss computation of single-subject pattern similarities and their statistical comparison at the within-person to the between-group level as well as the illustration and interpretation of the results. This tutorial targets both novice and more experienced EEG researchers and aims to facilitate the usage of spectral pattern similarity analyses, making these methodologies more readily accessible for (developmental) cognitive neuroscientists