The orthogonally aligned dark halo of an edge-on lensing galaxy in the Hubble Frontier Fields: a challenge for modified gravity

postprin

Hubble Frontier Field Free-form Mass Mapping of the Massive Multiple-merging Cluster MACSJ0717.5+3745

published_or_final_versio

Hubble Frontier Field Free-form Mass Mapping of the Massive Multiple-merging Cluster MACSJ0717.5+3745

published_or_final_versio

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\tilde\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\mathcal{N}=4$ super-Yang-Mills theory, $\Omega^{(1)}$ and $\Omega^{(2)}$. The derivative of $\Omega^{(2)}$ with respect to one of the conformal invariants yields $\tilde\Phi_6$, while another first-order differential operator applied to $\tilde\Phi_6$ yields $\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\mathcal{N}=4$ super-Yang-Mills.Comment: 18 pages, 2 figure

New differential equations for on-shell loop integrals

We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N=4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N=4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.Comment: 39 pages, 8 figures; v2: typos corrected, definition of harmonic polylogarithms adde

Symbols of One-Loop Integrals From Mixed Tate Motives

We use a result on mixed Tate motives due to Goncharov (arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop 2m-gon integral in 2m dimensions may be read off directly from its Feynman parameterization. The algorithm proceeds via recursion in m seeded by the well-known box integrals in four dimensions. As a simple application of this method we write down the symbol of a three-mass hexagon integral in six dimensions.Comment: 13 pages, v2: minor typos correcte

On form factors in N=4 sym

In this paper we study the form factors for the half-BPS operators $\mathcal{O}^{(n)}_I$ and the $\mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $\mathcal{K}$ at first order of perturbation theory in $\mathcal{N}=4$ SYM theory at weak coupling. For all the objects we observe the exponentiation of the IR divergences with two anomalous dimensions: the cusp anomalous dimension and the collinear anomalous dimension. For the IR finite parts we obtain a similar situation as for the gluon scattering amplitudes, namely, apart from the case of $W^{AB}$ and $\mathcal{K}$ the finite part has some remainder function which we calculate up to the second order. It involves the generalized Goncharov polylogarithms of several variables. All the answers are expressed through the integrals related to the dual conformal invariant ones which might be a signal of integrable structure standing behind the form factors.Comment: 35 pages, 7 figures, LATEX2

Young Galaxy Candidates in the Hubble Frontier Fields. IV. MACS J1149.5+2223

We search for high-redshift dropout galaxies behind the Hubble Frontier Fields (HFF) galaxy cluster MACS J1149.5+2223, a powerful cosmic lens that has revealed a number of unique objects in its field. Using the deep images from the Hubble and Spitzer space telescopes, we find 11 galaxies at z > 7 in the MACS J1149.5+2223 cluster field, and 11 in its parallel field. The high-redshift nature of the bright z sime 9.6 galaxy MACS1149-JD, previously reported by Zheng et al., is further supported by non-detection in the extremely deep optical images from the HFF campaign. With the new photometry, the best photometric redshift solution for MACS1149-JD reduces slightly to z = 9.44 ± 0.12. The young galaxy has an estimated stellar mass of (7\pm 2)\times {10}^{8}\,{M}_{\odot }, and was formed at $z={13.2}_{-1.6}^{+1.9} when the universe was ≈300 Myr old. Data available for the first four HFF clusters have already enabled us to find faint galaxies to an intrinsic magnitude of {M}_{{UV}}\simeq -15.5, approximately a factor of 10 deeper than the parallel fields

The last of the simple remainders

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited