Recursion Relations for Conformal Blocks

In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension $\Delta$ of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in 1307.6856 for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current.Comment: 55 pages, 12 figures; v2 Typos corrected, conclusions changed, reference adde

Radial expansion for spinning conformal blocks

This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we explain how to write closed form recursion relations for the coefficients of the expansions. We study three examples of four point functions in detail: one vector and three scalars; two vectors and two scalars; two spin 2 tensors and two scalars. Finally, for the case of two external vectors, we also provide a more efficient way to generate the series expansion using the analytic structure of the blocks as a function of the scaling dimension of the exchanged operator.Comment: 42 pages, 17 figures, 7 Mathematica files, v2: minor changes in the text, typos correcte

Projectors and seed conformal blocks for traceless mixed-symmetry tensors

In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.Comment: 49 pages, 1 Mathematica notebook, many figures, v2: add reference

Fourier-Mukai transform for fine compactified Prym varieties

Consider a finite covering $\beta : C \to X$ of a smooth projective curve $X$ by a reduced, projective, planar curve $C$. Associated to two general polarizations on $C$, $q$ and $q'$, one can construct the corresponding compactified Prym varieties $\overline{\mathrm{P}}_\beta(q)$ and $\overline{\mathrm{P}}_\beta(q')$. Consider $\Gamma$ to be the group of line bundles whose torsion coincides with the order of $\beta$. In this article we construct a Fourier-Mukai transform between the derived categories of $\overline{\mathrm{P}}_\beta(q)$ and the $\Gamma$-equivariant derived category of $\overline{\mathrm{P}}_\beta(q')$. Hence, we obtain a derived equivalence between the $\mathrm{SL}(n,\mathbb{C})$-Hitchin fibre and its associated $\mathrm{PGL}(n,\mathbb{C})$-Hitchin fibre for a dense class of singular spectral curves. Our work then provides the extension of the Fourier-Mukai transform constructed by Arinkin and Melo-Rapagnetta-Viviani, which corresponds to autoduality of $\mathrm{GL}(n,\mathbb{C})$-Hitchin fibres in this class of singular spectral curves

Characterization of coherent structures in three-dimensional turbulent flows using the finite-size Lyapunov exponent

arXiv:1207.1975In this paper, we use the finite-size Lyapunov exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3D) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. 3D FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by the numerical solution of the primitive equations where two-dimensional (2D) turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3D character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2D turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3D character of the FSLE ridges shows. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Lyapunov analysis: from dynamical systems theory to applications'. © 2013 IOP Publishing Ltd.This work was supported by Ministerio de Economía y Competitividad (Spain) and Fondo Europeo de Desarrollo Regional through project FISICOS (FIS2007-60327). JHB acknowledges financial support of the Portuguese FCT (Foundation for Science and Technology) and Fundo Social Europeo (FSE/QREN/POPH) through the predoctoral grant SFRH/BD/63840/2009.N

Lagrangian Coherent Structures in three-dimensional flows

arXiv:1207.1975v1Lagrangian Coherent Structures (LCS) act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. In the case of oceanic flows, LCS are known to drive biological dynamics, from plankton to top predators, which stresses the importance of their characterization in realistic flows. Lyapunov exponents are useful tools to compute LCSs. In this paper we have used the Finite-Size Lyapunov Exponent (FSLE) to identify LCSs in two different types of three-dimensional turbulent velocity fields. First, in a canonical turbulent flow (channel flow between two parallel plates) the LCSs have a complex three-dimensional shape and are advected by the flow. Second, in an oceanographic setting (a regional simulation of the Benguela area) the LCSs also show a complex pattern on the horizontal but the small vertical velocities typical of oceanic flows result in a curtain-like shape.Supported by Ministerio de Econom a y Competitividad (Spain) and Fondo Europeo de Desarrollo Regional through projects FISICOS (FIS2007-60327). JHB acknowledges nancial support of the Portuguese FCT (Foundation for Science and Technology) and Fundo Social Europeu (FSE/QREN/POPH) through the predoctoral grant SFRH/BD/63840/2009.Peer reviewe

Evaluating the Efficacy of Value-driven Methods: A Controlled Experiment

A value model is an abstract representation of an organization and is used for capturing and describing the rationale of how the organization creates, delivers, and captures business value. Value-driven development methods use the notion of “economic value exchange” to define more efficient business strategies and align Information Systems with the organization goals. However, current value-driven methods are complex and there is not enough empirical evidence about which of the existing methods is more effective under what circumstances. This paper addresses this issue by presenting a controlled experiment aimed at comparing the Dynamic Value Description (DVD) method, which is a recently defined cognitive early requirements approach, with the well-known e3value method, with respect to their effectiveness, efficiency, perceived ease of use, perceived usefulness and intention to use. The results show that DVD has proved to be a promising method for specifying business value

Strategy map for protection of the biosphere reserve of the Iberian Meseta

UNESCO considered the cross-border region of the Iberian Plateau in 2015. In 2017, the project entitled "Iberian Landscape - Network of Rural Landscapes on the Border of the Douro: A Strategic Map of the Iberian Plateau" was approved by the POCTEP program of INTERREG. One of the project's actions is to develop a strategic map for this region. This paper presents the strategic map developed based on a set of challenges and a strategic vision for the region. This map was formalized in 4 strategic objectives, each one with its lines of action and a set of specific actions that support them.info:eu-repo/semantics/publishedVersio

Empresas estrangeiras e transbordamentos de produtividade na industria brasileira : 1997-2000

Orientador: Mariano Francisco LaplaneDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de EconomiaMestrad