Tailoring Three-Point Functions and Integrability III. Classical Tunneling

We compute three-point functions between one large classical operator and two large BPS operators at weak coupling. We consider operators made out of the scalars of N=4 SYM, dual to strings moving in the sphere. The three-point function exponentiates and can be thought of as a classical tunneling process in which the classical string-like operator decays into two classical BPS states. From an Integrability/Condensed Matter point of view, we simplified inner products of spin chain Bethe states in a classical limit corresponding to long wavelength excitations above the ferromagnetic vacuum. As a by-product we solved a new long-range Ising model in the thermodynamic limit.Comment: 37 pages, 10 figure

On holographic three point functions for GKP strings from integrability

Adapting the powerful integrability-based formalism invented previously for the calculation of gluon scattering amplitudes at strong coupling, we develop a method for computing the holographic three point functions for the large spin limit of Gubser-Klebanov- Polyakov (GKP) strings. Although many of the ideas from the gluon scattering problem can be transplanted with minor modifications, the fact that the information of the external states is now encoded in the singularities at the vertex insertion points necessitates several new techniques. Notably, we develop a new generalized Riemann bilinear identity, which allows one to express the area integral in terms of appropriate contour integrals in the presence of such singularities. We also give some general discussions on how semiclassical vertex operators for heavy string states should be constructed systematically from the solutions of the Hamilton-Jacobi equation.Comment: 62 pages;v2 Typos and equation (3.7) corrected. Clarifying remarks added in Section 4.1. Published version;v3 Minor errors found in version 2 are corrected. For explanation of the revision, see Erratum published in http://www.springerlink.com/content/m67055235407vx67/?MUD=M

Wave functions and correlation functions for GKP strings from integrability

We develop a general method of computing the contribution of the vertex operators to the semi-classical correlation functions of heavy string states, based on the state-operator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of the saddle point configuration around each vertex insertion point and can be applied to cases where the precise forms of the vertex operators are not known. As an important application, we compute the contributions of the vertex operators to the three-point functions of the large spin limit of the Gubser-Klebanov-Polyakov (GKP) strings in $AdS_3$ spacetime, left unevaluated in our previous work [arXiv:1110.3949] which initiated such a study. Combining with the finite part of the action already computed previously and with the newly evaluated divergent part of the action, we obtain finite three-point functions with the expected dependence of the target space boundary coordinates on the dilatation charge and the spin.Comment: 80 pages, 7 figures, v2: typos and minor errors corrected, a reference added, v3: typos and a reference corrected, published versio

Combinações entre cultivares, ambientes, preparo e cobertura do solo em características agronômicas de alface.

Objetivou-se identificar combinações entre cultivares, ambientes de cultivo e preparo e cobertura de solo capazes de melhorar o desempenho agronômico e aumentar a produtividade da cultura da alface em cultivo orgânico. A pesquisa foi conduzida na Universidade Federal do Acre, utilizando o delineamento experimental de blocos casualizados, com parcelas subdivididas para cada experimento (campo e casa de vegetação), com quatro repetições. Em cada experimento, três cultivares de alface (Simpson, Marisa e Vera), constituindo as sub-parcelas, foram sorteadas nas parcelas, representadas por quatro preparos e cobertura do solo (encanteiramento com cobertura de palha de arroz, polietileno prateado, solo descoberto e plantio direto). A produtividade comercial de alface foi de 12,3 t ha-1 em cultivo protegido e de 7,9 t ha-1 em campo. O cultivo protegido promoveu melhor desenvolvimento das plantas, caracterizado por maior massa da matéria fresca e seca da parte aérea, massa da matéria fresca comercial e melhor classificação comercial, além de promover bom desempenho agronômico e maior produtividade em qualquer um dos preparos de solo. As cultivares Simpson e Marisa apresentaram massa da matéria seca da parte aérea semelhante e superior à ‘Vera’, porém, o crescimento do caule da ‘Simpson’ foi elevado, caracterizando pendoamento precoce, fato que reduz sua qualidade comercial. As cultivares Marisa e Vera não alongaram o caule indicando serem tolerantes às condições ambientais de Rio Branco. A cobertura do solo com casca de arroz ou plástico prateado contribuiu para minimizar os efeitos climáticos prejudiciais ao cultivo da alface em campo. O plantio direto orgânico não diferiu do plantio em canteiro descoberto

Holographic three-point functions for short operators

We consider holographic three-point functions for operators dual to short string states at strong coupling in N=4 super Yang-Mills. We treat the states as point-like as they come in from the boundary but as strings in the interaction region in the bulk. The interaction position is determined by saddle point, which is equivalent to conservation of the canonical momentum for the interacting particles, and leads to conservation of their conformal charges. We further show that for large dimensions the rms size of the interaction region is small compared to the radius of curvature of the AdS space, but still large compared to the string Compton wave-length. Hence, one can approximate the string vertex operators as flat-space vertex operators with a definite momentum, which depends on the conformal and R-charges of the operator. We then argue that the string vertex operator dual to a primary operator is chosen by satisfying a twisted version of Q^L=Q^R, up to spurious terms. This leads to a unique choice for a scalar vertex operator with the appropriate charges at the first massive level. We then comment on some features of the corresponding three-point functions, including the application of these results to Konishi operators.Comment: 24 pages; v2: References added, typos fixed, minor change

Intimate partner violence: a study in men and women from six European countries

OBJECTIVES: We aimed to assess intimate partner violence (IPV) among men and women from six cities in six European countries. METHODS: Four IPV types were measured in a population-based multicentre study of adults (18-64 years; n = 3,496). Sex- and city-differences in past year prevalence were examined considering victims, perpetrators or both and considering violent acts' severity and repetition. RESULTS: Male victimization of psychological aggression ranged from 48.8 % (Porto) to 71.8 % (Athens) and female victimization from 46.4 % (Budapest) to 70.5 % (Athens). Male and female victimization of sexual coercion ranged from 5.4 and 8.9 %, respectively, in Budapest to 27.1 and 25.3 % in Stuttgart. Male and female victims of physical assault ranged from 9.7 and 8.5 %, respectively, in Porto, to 31.2 and 23.1 % in Athens. Male victims of injury were 2.7 % in Östersund and 6.3 % in London and female victims were 1.4 % in Östersund and 8.5 % in Stuttgart. IPV differed significantly across cities (p < 0.05). Men and women predominantly experienced IPV as both victims and perpetrators with few significant sex-differences within cities. CONCLUSIONS: Results support the need to consider men and women as both potential victims and perpetrators when approaching IPV