Superconformal Coset Equivalence from Level-Rank Duality

We construct a one-to-one map between the primary fields of the N=2 superconformal Kazama-Suzuki models G(m,n,k) and G(k,n,m) based on complex Grassmannian cosets, using level-rank duality of Wess-Zumino-Witten models. We then show that conformal weights, superconformal U(1) charges, modular transformation matrices, and fusion rules are preserved under this map, providing strong evidence for the equivalence of these coset models.Comment: 25 pages, harvmac, no figures, added referenc

Simple Current Actions of Cyclic Groups

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k^2 (where k is a divisor of n) or 3k^2 if the spin of the simple current is half-integral and k is odd.Comment: Added reference, minor change

Automorphism Modular Invariants of Current Algebras

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac--Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.Comment: 32 pages, plain Te

Simple-Current Symmetries, Rank-Level Duality, and Linear Skein Relations for Chern-Simons Graphs

A previously proposed two-step algorithm for calculating the expectation values of Chern-Simons graphs fails to determine certain crucial signs. The step which involves calculating tetrahedra by solving certain non- linear equations is repaired by introducing additional linear equations. As a first step towards a new algorithm for general graphs we find useful linear equations for those special graphs which support knots and links. Using the improved set of equations for tetrahedra we examine the symmetries between tetrahedra generated by arbitrary simple currents. Along the way we uncover the classical origin of simple-current charges. The improved skein relations also lead to exact identities between planar tetrahedra in level $K$ $G(N)$ and level $N$ $G(K)$ CS theories, where $G(N)$ denotes a classical group. These results are recast as identities for quantum $6j$-symbols and WZW braid matrices. We obtain the transformation properties of arbitrary graphs and links under simple current symmetries and rank-level duality. For links with knotted components this requires precise control of the braid eigenvalue permutation signs, which we obtain from plethysm and an explicit expression for the (multiplicity free) signs, valid for all compact gauge groups and all fusion products.Comment: 58 pages, BRX-TH-30

A Minimal Superstring Standard Model I: Flat Directions

Three family SU(3)_C x SU(2)_L x U(1)_Y string models in several constructions generically possess two features: (i) an extra local anomalous U(1)_A and (ii) numerous (often fractionally charged) exotic particles beyond those in the minimal supersymmetric model (MSSM). Recently, we demonstrated that the observable sector effective field theory of such a free fermionic string model can reduce to that of the MSSM, with the standard observable gauge group being just SU(3)_C x SU(2)_L x U(1)_Y and the SU(3)_C x SU(2)_L x U(1)_Y-charged spectrum of the observable sector consisting solely of the MSSM spectrum. An example of a model with this property was shown. We continue our investigation of this model by presenting a large set of different flat directions of the same model that all produce the MSSM spectrum. Our results suggest that even after imposing the conditions for the decoupling of exotic states, there may remain sufficient freedom to satisfy the remaining phenomenological constraints imposed by the observed data.Comment: 64 pages. Latex. Revisions to match version in Int. J. Mod. Physics

On the numerical integration of isogeometric interface elements

Zero-thickness interface elements are commonly used in computational mechanics to model material interfaces or to introduce discontinuities. The latter class requires the existence of a non-compliant interface prior to the onset of fracture initiation. This is accomplished by assigning a high dummy stiffness to the interface prior to cracking. This dummy stiffness is known to introduce oscillations in the traction profile when using Gauss quadrature for the interface elements, but these oscillations are removed when resorting to a Newton-Cotes integration scheme 1. The traction oscillations are aggravated for interface elements that use B-splines or non-uniform rational B-splines as basis functions (isogeometric interface elements), and worse, do not disappear when using Newton-Cotes quadrature. An analysis is presented of this phenomenon, including eigenvalue analyses, and it appears that the use of lumped integration (at the control points) is the only way to avoid the oscillations in isogeometric interface elements. New findings have also been obtained for standard interface elements, for example that oscillations occur in the relative displacements at the interface irrespective of the value of the dummy stiffness

Moving towards 100% renewable electricity in Europe & North Africa by 2050

In spring 2010, European and international climate experts at PwC, the European Climate Forum, the Potsdam Institute for Climate Impact Research and the International Institute for Applied System Analysis published 100% Renewable Electricity - A roadmap to 2050 for Europe and North Africa. The report examined the potential for powering Europe and North Africa with renewable electricity exclusively by 2050. It set out a series of financial, market, infrastructure and government policy steps that would need to occur if such a "what if" vision was to be achieved. Now, a year on, this latest report provides a complementary analysis to the original roadmap. PwC, the Potsdam Institute for Climate Impact Research and the International Institute for Applied System Analysis, look at whether the vision of 100% renewable electricity has moved closer or further away as a result of current and recent developments over the last 12 months. The report, intended to support the wider debate in this area, examines five areas that are most critical to achieving progress and, through the lens of these five areas, looks at the impact of recent and current events

Lectures on conformal field theory and Kac-Moody algebras

This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.Comment: 59 pages, LaTeX2e, extended version of lectures given at the Graduate Course on Conformal Field Theory and Integrable Models (Budapest, August 1996), to appear in Springer Lecture Notes in Physic

River gauging at global scale using optical and passive microwave remote sensing

Recent discharge observations are lacking for most rivers globally. Discharge can be estimated from remotely sensed floodplain and channel inundation area, but there is currently no method that can be automatically extended to many rivers. We examined whether automated monitoring is feasible by statistically relating inundation estimates from moderate to coarse (>0.05°) resolution remote sensing to monthly station discharge records. Inundation extents were derived from optical MODIS data and passive microwave sensors, and compared to monthly discharge records from over 8000 gauging stations and satellite altimetry observations for 442 reaches of large rivers. An automated statistical method selected grid cells to construct “satellite gauging reaches” (SGRs). MODIS SGRs were generally more accurate than passive microwave SGRs, but there were complementary strengths. The rivers widely varied in size, regime, and morphology. As expected performance was low (R  0.6. The best results (R > 0.9) were obtained for large unregulated lowland rivers, particularly in tropical and boreal regions. Relatively poor results were obtained in arid regions, where flow pulses are few and recede rapidly, and in temperate regions, where many rivers are modified and contained. Provided discharge variations produce clear changes in inundated area and gauge records are available for part of the satellite record, SGRs can retrieve monthly river discharge values back to around 1998 and up to present

Revisiting large-scale interception patterns constrained by a synthesis of global experimental data

Rainfall interception loss remains one of the most uncertain fluxes in the global water balance, hindering water management in forested regions and precluding an accurate formulation in climate models. Here, a synthesis of interception loss data from past field experiments conducted worldwide is performed, resulting in a meta-analysis comprising 166 forest sites and 17 agricultural plots. This meta-analysis is used to constrain a global process-based model driven by satellite-observed vegetation dynamics, potential evaporation and precipitation. The model considers sub-grid heterogeneity and vegetation dynamics and formulates rainfall interception for tall and short vegetation separately. A global, 40-year (1980–2019), 0.1∘ spatial resolution, daily temporal resolution dataset is created, analysed and validated against in situ data. The validation shows a good consistency between the modelled interception and field observations over tall vegetation, both in terms of correlations and bias. While an underestimation is found in short vegetation, the degree to which it responds to in situ representativeness errors and difficulties inherent to the measurement of interception in short vegetated ecosystems is unclear. Global estimates are compared to existing datasets, showing overall comparable patterns. According to our findings, global interception averages to 73.81 mm yr−1 or 10.96 × 103 km3 yr−1, accounting for 10.53 % of continental rainfall and approximately 14.06 % of terrestrial evaporation. The seasonal variability of interception follows the annual cycle of canopy cover, precipitation, and atmospheric demand for water. Tropical rainforests show low intra-annual vegetation variability, and seasonal patterns are dictated by rainfall. Interception shows a strong variance among vegetation types and biomes, supported by both the modelling and the meta-analysis of field data. The global synthesis of field observations and the new global interception dataset will serve as a benchmark for future investigations and facilitate large-scale hydrological and climate research.</p