The numerical approach to quantum field theory in a non-commutative space

Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is presented, and their implications are reviewed. In addition, we also discuss how related numerical techniques have been recently applied in computer simulations of dimensionally reduced supersymmetric theories.Comment: 15 pages, 6 figures, invited talk presented at the Humboldt Kolleg "Open Problems in Theoretical Physics: the Issue of Quantum Space-Time", to appear in the proceedings of the Corfu Summer Institute 2015 "School and Workshops on Elementary Particle Physics and Gravity" (Corfu, Greece, 1-27 September 2015

Thermodynamics of the strongly interacting gluon plasma in the large-N limit

We report on our recent study of equilibrium thermodynamic observables in SU(N) gauge theories with N=3, 4, 5, 6 and 8 colors at temperatures T in the range from 0.8 T_c to 3.4 T_c (where T_c denotes the critical deconfinement temperature). The results, which show a very weak dependence on the number of colors, are compared with gauge/gravity models of the QCD plasma, including the improved holographic QCD model proposed by Kiritsis and collaborators, and with the supergravity prediction for the entropy density deficit. Furthermore, we investigate the possibility that the trace anomaly may receive contributions proportional to T^2 at temperatures close to T_c. Finally, we present the extrapolated results for the pressure, trace anomaly, energy and entropy densities in the limit for N going to infinity.Comment: 7 pages, 8 eps figures, presented at the XXVII International Symposium on Lattice Field Theory, July 26-31 2009, Peking University, Beijing, China; v2: added reference

Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere

We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The Nature of Context-Sensitive Solutions, Stakeholder Involvement and Critical Issues in the Urban Context

Over the last several decades many transportation and planning agencies have experienced conflicting demands emerging from the need to develop projects in an expeditious manner while at the same time involving stakeholders in the decision-making process, which sometimes is perceived as slowing project delivery and/or increasing costs. Given this tension between apparently conflicting demands, it is important to understand how the stakeholder involvement is being carried out and what best practices may be recommended. This study examines the issue in the context of a relatively new policy framework – Context Sensitive Solutions (CSS) – which supports the early integration of stakeholders into the planning process. The report pays particular attention to stakeholders’ involvement in projects within urban centers, where there is likely to be more complexity, both in terms of the number of stakeholders and end users affected. CSS is a relatively new process and not consistently interpreted or applied across states and/or agencies. The literature suggests that an underlying assumption when applying CSS principles to community involvement processes is that stakeholders are empowered through clear policies and procedures directed towards their participation. In our research, we found that the extent to which public agencies apply the CSS framework and involve and respond to stakeholders depends on each agency\u27s interest to engage the public in the deliberation process to find the best-fit project for a community. It is likely that the increased integration of stakeholders into the planning and project development process will not become a state of practice until the benefits flowing from community involvement are clearly understood by the agency staff. The CSS literature describes many benefits associated with comprehensive stakeholder engagement, including gaining constituents\u27 buy-in and support for project financing. A movement toward standardizing CSS policies and directives across the country will facilitate a public discussion about the benefits of engaging communities into the project design phase and away from solely expert-based designs. In addition, there are a number of stakeholder involvement practices that, if adopted, could expedite the integration of communities\u27 views and values in the decision-making process, while at the same time minimizing the chances of protracted consultation processes, time delays and additional costs

Casimir scaling and renormalization of Polyakov loops in large-N gauge theories

We study Casimir scaling and renormalization properties of Polyakov loops in different irreducible representations in SU(N) gauge theories; in particular, we investigate the approach to the large-N limit, by performing lattice simulations of Yang-Mills theories with an increasing number of colors, from 2 to 6. We consider the twelve lowest irreducible representations for each gauge group, and find strong numerical evidence for nearly perfect Casimir scaling of the bare Polyakov loops in the deconfined phase. Then we discuss the temperature dependence of renormalized loops, which is found to be qualitatively and quantitatively very similar for the various gauge groups. In particular, close to the deconfinement transition, the renormalized Polyakov loop increases with the temperature, and its logarithm reveals a characteristic dependence on the inverse of the square of the temperature. At higher temperatures, the renormalized Polyakov loop overshoots one, reaches a maximum, and then starts decreasing, in agreement with weak-coupling predictions. The implications of these findings are discussed.Comment: 1+33 pages, 14 figures; v2: expanded discussion in sections 2 and 3, added references: version published in JHE