An Extension of the Character Ring of sl(3) and Its Quantisation

We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring $Z[\tilde{W}]$ of the extended affine Weyl group of $\hat{sl}(3)_k$ at $k\not \in Q$. The `quantised' version at rational level $k+3=3/p$ realises the fusion rules of a WZW conformal field theory based on admissible representations of $\hat{sl}(3)_k$.Comment: contains two TeX files: main file using harvmac.tex, amssym.def, amssym.tex, 35p.; file with figures using XY-pic package, 4p; v2: minor corrections, Note adde

Non-critical string pentagon equations and their solutions

We derive pentagon type relations for the 3-point boundary tachyon correlation functions in the non-critical open string theory with generic c_{matter} < 1 and study their solutions in the case of FZZ branes. A new general formula for the Liouville 3-point factor is derived.Comment: 18 pages, harvmac; misprints corrected, section 3.2 extended, a new general formula for the Liouville 3-point factor adde

Conformal Field Theories, Graphs and Quantum Algebras

This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize modular invariance for a given RCFT in the presence of various types of boundary conditions --open, twisted-- are encoded in a system of integer multiplicities that form matrix representations of fusion-like algebras. These multiplicities are also the combinatorial data that enable one to construct an abstract ``quantum'' algebra, whose $6j$- and $3j$-symbols contain essential information on the Operator Product Algebra of the RCFT and are part of a cell system, subject to pentagonal identities. It looks quite plausible that the classification of a wide class of RCFT amounts to a classification of ``Weak $C^*$- Hopf algebras''.Comment: 23 pages, 12 figures, LateX. To appear in MATHPHYS ODYSSEY 2001 --Integrable Models and Beyond, ed. M. Kashiwara and T. Miwa, Progress in Math., Birkhauser. References and comments adde

On the crossing relation in the presence of defects

The OPE of local operators in the presence of defect lines is considered both in the rational CFT and the $c>25$ Virasoro (Liouville) theory. The duality transformation of the 4-point function with inserted defect operators is explicitly computed. The two channels of the correlator reproduce the expectation values of the Wilson and 't Hooft operators, recently discussed in Liouville theory in relation to the AGT conjecture.Comment: TEX file with harvmac; v3: JHEP versio

Projected Heat-Related Mortality in the U.S. Urban Northeast

Increased heat-related mortality is projected to be among the major impacts of climate change on human health, and the United States urban Northeast region is likely to be particularly vulnerable. In support of regional adaptation planning, quantitative information is needed on potential future health responses at the urban and regional scales. Here, we present future projections of heat-related mortality in Boston, New York and Philadelphia utilizing downscaled next-generation climate models and Representative Concentration Pathways (RCPs) developed in support of the Intergovernmental Panel on Climate Change (IPCC)’s Fifth Assessment Report (AR5). Our analyses reveal that heat-related mortality rates per 100,000 of population during the baseline period between 1985 and 2006 were highest in Philadelphia followed by New York City and Boston. However, projected heat-related mortality rates in the 2020s, 2050s and 2080s were highest in New York City followed by Philadelphia and Boston. This study may be of value in developing strategies for reducing the future impacts of heat and building climate change resilience in the urban Northeast region

Dietary fat intake as a risk factor for the development of diabetes. Multinational, multicenter study of the Mediterranean Group for the Study of Diabetes (MGDS)

In the context of the Multinational MGSD Nutrition Study, three groups of subjects were studied: 204 subjects with recently diagnosed diabetes(RDM),42subjectswithundiagnoseddiabetes(UDM)(AmericanDiabetesAssociation criteria—fasting plasma glucose [FPG] 126 mg/dl), and 55 subjects with impaired fasting glucose(IFG)(FPG 110and126mg/dl).Eachgroupwascomparedwithacontrolgroupof nondiabetic subjects, matched one by one for center, sex, age, and BMI. Nutritional habits were evaluated by a dietary history method, validated against the 3-day diet diary. In RDM, the questionnaire referred to the nutritional habits before the diagnosis of diabetes. Demographic data were collected, and anthropometrical and biochemical measurements were taken. RESULTS— Compared with control subjects, RDM more frequently had a family history of diabetes(49.0vs.14.2%;P0.001),exercisedless(exerciseindex53.5vs.64.4;P0.01),and more frequently had sedentary professions (47.5 vs. 27.4%; P 0.001). Carbohydrates contributed less to their energy intake (53.5 vs. 55.1%; P 0.05), whereas total fat (30.2 0.5 vs. 27.8 0.5%; P 0.001) and animal fat (12.2 0.3 vs. 10.8 0.3%; P 0.01) contributed moreandtheplant-to-animalfatratiowaslower(1.50.1vs.1.80.1;P0.01).UDMmore frequentlyhadafamilyhistoryofdiabetes(38.1vs.19.0%;P0.05)andsedentaryprofessions (58.5vs.34.1%;P0.05),carbohydratescontributedlesstotheirenergyintake(47.61.7vs. 52.81.4%;P0.05),totalfat(34.71.5vs.30.41.2%;P0.05)andanimalfat(14.2 0.9 vs. 10.6 0.7%; P 0.05) contributed more, and the plant-to-animal fat ratio was lower (1.6 0.2 vs. 2.3 0.4; P 0.05). IFG differed only in the prevalence of family history of diabetes (32.7 vs. 16.4%; P 0.05). CONCLUSIONS— Our data support the view that increased animal fat intake is associated with the presence of diabetes

From conformal embeddings to quantum symmetries: an exceptional SU(4) example

We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a quantum graph. For known examples, the corresponding modular invariant partition function, which is sometimes associated with a conformal embedding, provides enough information to recover the whole structure. We illustrate these notions with the example of the conformal embedding of SU(4) at level 4 into Spin(15) at level 1, leading to the exceptional quantum graph E4(SU(4)).Comment: 22 pages, 3 color figures. Version 2: We changed the color of figures (ps files) in such a way that they are still understood when converted to gray levels. Version 3: Several references have been adde

The Virtue of Defects in 4D Gauge Theories and 2D CFTs

We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories - which we construct - and loop operators and domain wall operators in four dimensional N=2 supersymmetric gauge theories on S^4. Our computation of the correlation functions in Liouville/Toda theory in the presence of topological defect operators, which are supported on curves on the Riemann surface, yields the exact answer for the partition function of four dimensional gauge theories in the presence of various walls and loop operators; results which we can quantitatively substantiate with an independent gauge theory analysis. As an interesting outcome of this work for two dimensional conformal field theories, we prove that topological defect operators and the Verlinde loop operators are different descriptions of the same operators.Comment: 59 pages, latex; v2 corrections to some formula

Integrable Lattice Realizations of Conformal Twisted Boundary Conditions

We construct integrable realizations of conformal twisted boundary conditions for ^sl(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical A-D-E lattice models with positive spectral parameter. The integrable seam boundary conditions are labelled by (r,s,\zeta) in (A_{g-2},A_{g-1},\Gamma) where \Gamma is the group of automorphisms of G and g is the Coxeter number of G. Taking symmetries into account, these are identified with conformal twisted boundary conditions of Petkova and Zuber labelled by (a,b,\gamma) in (A_{g-2}xG, A_{g-2}xG,Z_2) and associated with nodes of the minimal analog of the Ocneanu quantum graph. Our results are illustrated using the Ising (A_2,A_3) and 3-state Potts (A_4,D_4) models.Comment: 11 pages, LaTeX. Added some reference

't Hooft Operators in Gauge Theory from Toda CFT

We construct loop operators in two dimensional Toda CFT and calculate with them the exact expectation value of certain supersymmetric 't Hooft and dyonic loop operators in four dimensional \Ncal=2 gauge theories with SU(N) gauge group. Explicit formulae for 't Hooft and dyonic operators in \Ncal=2^* and \Ncal=2 conformal SQCD with SU(N) gauge group are presented. We also briefly speculate on the Toda CFT realization of arbitrary loop operators in these gauge theories in terms of topological web operators in Toda CFT.Comment: 49 pages, LaTeX. Typos fixed, references adde