Dilogarithm Identities in Conformal Field Theory

Dilogarithm identities for the central charges and conformal dimensions exist for at least large classes of rational conformally invariant quantum field theories in two dimensions. In many cases, proofs are not yet known but the numerical and structural evidence is convincing. In particular, close relations exist to fusion rules and partition identities. We describe some examples and ideas, and present some conjectures useful for the classification of conformal theories. The mathematical structures seem to be dual to Thurston's program for the classification of 3-manifolds.Comment: 14 pages, BONN-preprint. (a few minor changes, two major corrections in chapter 3, namely: (3.10) only holds in the case of the A series, Goncharovs conjecture is not an equivalence but rather an implication and a theorem

Steps towards Lattice Virasoro Algebras: su(1,1)

An explicit construction is presented for the action of the su(1,1) subalgebra of the Virasoro algebra on path spaces for the c(2,q) minimal models. In the case of the Lee-Yang edge singularity, we show how this action already fixes the central charge of the full Virasoro algebra. For this case, we additionally construct a representation in terms of generators of the corresponding Temperley-Lieb algebra.Comment: 15 pages, plain TeX, 4 typos correcte

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate

T-systems and Y-systems in integrable systems

The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras with coefficients, periodicity conjectures of Zamolodchikov and others, dilogarithm identities in conformal field theory, difference analogue of L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem, AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and so forth. This review article is a collection of short reviews on these topics which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5, eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical review) also needs these correction

A global spectral library to characterize the world's soil

Soil provides ecosystem services, supports human health and habitation, stores carbon and regulates emissions of greenhouse gases. Unprecedented pressures on soil from degradation and urbanization are threatening agro-ecological balances and food security. It is important that we learn more about soil to sustainably manage and preserve it for future generations. To this end, we developed and analyzed a global soil visible-near infrared (vis-NIR) spectral library. It is currently the largest and most diverse database of its kind. We show that the information encoded in the spectra can describe soil composition and be associated to land cover and its global geographic distribution, which acts as a surrogate for global climate variability. We also show the usefulness of the global spectra for predicting soil attributes such as soil organic and inorganic carbon, clay, silt, sand and iron contents, cation exchange capacity, and pH. Using wavelets to treat the spectra, which were recorded in different laboratories using different spectrometers and methods, helped to improve the spectroscopic modelling. We found that modelling a diverse set of spectra with a machine learning algorithm can find the local relationships in the data to produce accurate predictions of soil properties. The spectroscopic models that we derived are parsimonious and robust, and using them we derived a harmonized global soil attribute dataset, which might serve to facilitate research on soil at the global scale. This spectroscopic approach should help to deal with the shortage of data on soil to better understand it and to meet the growing demand for information to assess and monitor soil at scales ranging from regional to global. New contributions to the library are encouraged so that this work and our collaboration might progress to develop a dynamic and easily updatable database with better global coverage. We hope that this work will reinvigorate our community's discussion towards larger, more coordinated collaborations. We also hope that use of the database will deepen our understanding of soil so that we might sustainably manage it and extend the research outcomes of the soil, earth and environmental sciences towards applications that we have not yet dreamed of

Gepner Modelle und W-Algebren

SIGLEAvailable from TIB Hannover: RN 4852(92-20) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman