Bonus scaling and BCFW in N=7 supergravity

In search of natural building blocks for supergravity amplitudes, a tentative criteria is term-by-term bonus z^-2 large momentum scaling. For a given choice of deformation legs, we present such an expansion in the form of a BCFW representation in N=7 supergravity based on a special shift. We will show that this improved scaling behavior, with respect to the fully N=8 representation, is due to its automatic incorporation of the so called bonus relations.Comment: 16 pages, 2 figure

Localization of electric field distribution in graded core-shell metamaterials

The local electric field distribution has been investigated in a core-shell cylindrical metamaterial structure under the illumination of a uniform incident optical field. The structure consists of a homogeneous dielectric core, a shell of graded metal-dielectric metamaterial, embedded in a uniform matrix. In the quasi-static limit, the permittivity of the metamaterial is given by the graded Drude model. The local electric potentials and hence the electric fields have been derived exactly and analytically in terms of hyper-geometric functions. Our results showed that the peak of the electric field inside the cylindrical shell can be confined in a desired position by varying the frequency of the optical field and the parameters of the graded profiles. Thus, by fabricating graded metamaterials, it is possible to control electric field distribution spatially. We offer an intuitive explanation for the gradation-controlled electric field distribution

Extreme Candidates as the Beneficent Spoiler? Range Effect in the Plurality Voting System

How does the entrance of radical candidates influence election results? Conventional wisdom suggests that extreme candidates merely split the votes. Based on the range effect theory in cognitive psychology, we hypothesize that the entrance of an extreme candidate reframes the endpoints of the ideological spectrum among available candidates, which makes the moderate one on the same side to be perceived by the voters as even more moderate. Through two survey experiments in the United States and Taiwan, we provide empirical support for range effect in the vote choice in the plurality system. The results imply that a mainstream party can, even without changing its own manifesto, benefit from the entrance of its radical counterpart; it explains why the mainstream party may choose cooperation strategically. Our findings also challenge the assumption in regression models that the perceived ideological positions of candidates are independent of each other

Anatomy of Geodesic Witten Diagrams

We revisit the so-called "Geodesic Witten Diagrams" (GWDs) \cite{ScalarGWD}, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.Comment: 40 pages, 4 figures, v2: typos corrected, references added, Appendix E and a Mellin space discussion added, v3: typos correcte

Towards Spinning Mellin Amplitudes

We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.Comment: 32 pages, 2 figures, v2: typos corrected, clarification added, references updated, to appear in NP