BPS dyons and Hesse flow

We revisit BPS solutions to classical N=2 low energy effective gauge theories. It is shown that the BPS equations can be solved in full generality by the introduction of a Hesse potential, a symplectic analog of the holomorphic prepotential. We explain how for non-spherically symmetric, non-mutually local solutions, the notion of attractor flow generalizes to gradient flow with respect to the Hesse potential. Furthermore we show that in general there is a non-trivial magnetic complement to this flow equation that is sourced by the momentum current in the solution.Comment: 25 pages, references adde

Correlation function of null polygonal Wilson loops with local operators

We consider the correlator of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or the chiral primary scalar) in planar N =4 super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n-11 conformal ratios. The first non-trivial case is n=4 when F depends on just one conformal ratio \zeta. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the `t Hooft coupling \lambda. We compute F(\zeta,\lambda) at leading order in both the strong coupling regime (using semiclassical AdS5 x S5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in arXiv:1007.3243.Comment: 36 pages, 2 figure

Deconstructing Conformal Blocks in 4D CFT

We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few \u201cseed\u201d correlators, simplifying dramatically the computation needed to bootstrap tensor correlators. \ua9 2015, The Author(s)

From correlation functions to scattering amplitudes

We study the correlators of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the loop corrections by means of Lagrangian insertions. The divergences resulting from the light-cone limit are regularized by changing the dimension of the integration measure over the insertion points. Switching from coordinates to dual momenta, we show that the logarithm of the correlator is identical with twice the logarithm of the matching MHV gluon scattering amplitude. We present a number of examples of this new relation, at one and two loops.Comment: typos corrected, references adde

Closed Strings and Moduli in AdS3/CFT2

String theory on AdS3×S3×T4 has 20 moduli. We investigate how the perturbative closed string spectrum changes as we move around this moduli space in both the RR and NSNS flux backgrounds. We find that, at weak string coupling, only four of the moduli affect the energies. In the RR background the only effect of these moduli is to change the radius of curvature of the background. On the other hand, in the NSNS background, the moduli introduce worldsheet interactions which enable the use of integrability methods to solve the spectral problem. Our results show that the worldsheet theory is integrable across the 20 dimensional moduli space

Expression of vascular endothelial growth factor mRNA in non-small-cell lung carcinomas

The vascular endothelial growth factor (VEGF) has been shown to be strictly related to vascular permeability and endothelial cell growth under physiological and pathological conditions. In tumour development and progression, VEGF plays a pivotal role in the development of the tumoral vascular network, and useful information in the progression of human cancer can be obtained by analysing the vascular endothelial growth factor expression of the tumours. In this study, we investigated the vascular endothelial growth factor transcript expression in non-small-cell lung carcinomas to evaluate the significance of this factor in a group of cancers in which the vascular pattern has been shown to significantly affect progression. Surgical samples of 42 patients with NSCLC were studied using reverse transcription polymerase chain reaction (PCR) analysis and in situ hybridization. Thirty-three out of 42 cases (78.6%) showed VEGF transcript expression predominantly as transcripts for the secretory forms of VEGF (isoforms 121 and 165). In situ hybridization, performed on 24 out of 42 samples, showed that the VEGF transcript expression was in several cases present in the cytoplasm both of neoplastic and normal cells, even if the VEGF mRNA was less expressed in the corresponding non-tumoral part. The VEGF 121 expression was associated with hilar and/or mediastinal nodal involvement (P = 0.02), and, taken together, the VEGF isoforms were shown to significantly influence overall (P = 0.02) and disease-free survival (P = 0.03). As a regulator of tumour angiogenesis, VEGF may represent a useful indicator of progression and poor prognosis in non-small-cell lung carcinomas. © 1999 Cancer Research Campaig

All-mass n-gon integrals in n dimensions

We explore the correspondence between one-loop Feynman integrals and (hyperbolic) simplicial geometry to describe the "all-mass" case: integrals with generic external and internal masses. Specifically, we focus on $n$-particle integrals in exactly $n$ space-time dimensions, as these integrals have particularly nice geometric properties and respect a dual conformal symmetry. In four dimensions, we leverage this geometric connection to give a concise dilogarithmic expression for the all-mass box in terms of the Murakami-Yano formula. In five dimensions, we use a generalized Gauss-Bonnet theorem to derive a similar dilogarithmic expression for the all-mass pentagon. We also use the Schl\"afli formula to write down the symbol of these integrals for all $n$. Finally, we discuss how the geometry behind these formulas depends on space-time signature, and we gather together many results related to these integrals from the mathematics and physics literature.Comment: 49 pages, 8 figure