Symmetry breaking boundary conditions and WZW orbifolds

Symmetry breaking boundary conditions for WZW theories are discussed. We derive explicit formulae for the reflection coefficients in the presence of boundary conditions that preserve only an orbifold subalgebra with respect to an involutive automorphism of the chiral algebra. The characters and modular transformations of the corresponding orbifold theories are computed. Both inner and outer automorphisms are treated.Comment: 39 pages, LaTeX2

About the "away goals rule" in association football:Does scrapping the rule increase the fairness of the game?

The present study analyzes all major international football tournaments organized by UEFA and CONMEBOL during a period of 30 years to assess the impact of the away goals rule (AGR). The study takes advantage of natural experiment given by the differentiated application of the AGR by both confederations, in order to assess the efficacy and the consequences of the rule in terms of both the total amount of goals being scored (the original intention of the rule) and the teams that progressed onto the next stages. The results show that the AGR seems to have failed to fulfill its original goal of increasing both scoring by teams playing away and scoring in general. The AGR is found to have a significant impact favoring the chances of the team starting the series at home. However, it still does not translate into a higher probability of progressing onto the next stage than the team closing the series at home. Closing the series at home has an intrinsic advantage, which is only countered, although not completely, by the impact of the AGR. Regarding tiebreakers, we observe that closing the series at home has a positive impact no matter whether overtimes with AGR or penalty shootouts are used as tiebreakers. However, playing an overtime, when no AGR is set in place has a determining influence favoring the team closing the series at home

KMS, etc

A general form of the ``Wick rotation'', starting from imaginary-time Green functions of quantum-mechanical systems in thermal equilibrium at positive temperature, is established. Extending work of H. Araki, the role of the KMS condition and of an associated anti-unitary symmetry operation, the ``modular conjugation'', in constructing analytic continuations of Green functions from real- to imaginary times, and back, is clarified. The relationship between the KMS condition for the vacuum with respect to Lorentz boosts, on one hand, and the spin-statistics connection and the PCT theorem, on the other hand, in local, relativistic quantum field theory is recalled. General results on the reconstruction of local quantum theories in various non-trivial gravitational backgrounds from ``Euclidian amplitudes'' are presented. In particular, a general form of the KMS condition is proposed and applied, e.g., to the Unruh- and the Hawking effects. This paper is dedicated to Huzihiro Araki on the occasion of his seventieth birthday, with admiration, affection and best wishes.Comment: 56 pages, submitted to J. Math. Phy

From riding to driving:The effects of the COVID-19 pandemic on public transit in Metro Vancouver

This study analyzed a panel-based dataset to understand the effect of COVID-19 on transport behavior in Metro Vancouver, Canada, between December 2020 and May 2021. Findings from the sample indicate a decline in transit users compared to pre-pandemic levels and an increase in car use. On the other hand, we saw a shift to a more positive perception of transit in May 2021, while also capturing an increase in perceived levels of crowding. The study underscores the necessity for transit agencies to focus on instilling the feeling of safety among the population, as the majority of those who have not used transit since the beginning of the pandemic reported their willingness to return only with widespread vaccination, community immunity, or other broad successful treatments

Network Friendly P2P-TV: The Napa-Wine Approach

DEMO Sessio

Modifications to the Machine Optics of BESSY II Necessitated by the EMIL Project

The Helmholtz Zentrum Berlin and the Max Planck Society are going to build a new dedicated X ray beam line at the synchrotron light source BESSY II which will be used for analyzing materials for renewable energy generation. The new large scale project has been dubbed EMIL. In this document we present the modifications to the machine optics and to what extent these changes affect the performance of BESSY I

Charges of Exceptionally Twisted Branes

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.Comment: 19 pages, 2 figures, LaTex2e, complete proofs of all statements, updated bibliograph

The charges of a twisted brane

The charges of the twisted D-branes of certain WZW models are determined. The twisted D-branes are labelled by twisted representations of the affine algebra, and their charge is simply the ground state multiplicity of the twisted representation. It is shown that the resulting charge group is isomorphic to the charge group of the untwisted branes, as had been anticipated from a K-theory calculation. Our arguments rely on a number of non-trivial Lie theoretic identities.Comment: 27 pages, 1 figure, harvmac (b