Hexagon OPE Resummation and Multi-Regge Kinematics

We analyse the OPE contribution of gluon bound states in the double scaling limit of the hexagonal Wilson loop in planar N=4 super Yang-Mills theory. We provide a systematic procedure for perturbatively resumming the contributions from single-particle bound states of gluons and expressing the result order by order in terms of two-variable polylogarithms. We also analyse certain contributions from two-particle gluon bound states and find that, after analytic continuation to the $2\to 4$ Mandelstam region and passing to multi-Regge kinematics (MRK), only the single-particle gluon bound states contribute. From this double-scaled version of MRK we are able to reconstruct the full hexagon remainder function in MRK up to five loops by invoking single-valuedness of the results.Comment: 29 pages, 3 figures, 4 ancillary file

The Double Pentaladder Integral to All Orders

We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N=4 super-Yang-Mills theory. We provide exact, finite-coupling formulas for the basic double pentaladder integrals as a single Mellin integral over hypergeometric functions. For particular choices of the dual conformal cross ratios, we can evaluate the integral at weak coupling to high loop orders in terms of multiple polylogarithms. We argue that the integrals are exponentially suppressed at strong coupling. We describe the space of functions that contains all such double pentaladder integrals and their derivatives, or coproducts. This space, a prototype for the space of Steinmann hexagon functions, has a simple algebraic structure, which we elucidate by considering a particular discontinuity of the functions that localizes the Mellin integral and collapses the relevant symbol alphabet. This function space is endowed with a coaction, both perturbatively and at finite coupling, which mixes the independent solutions of the hypergeometric differential equation and constructively realizes a coaction principle of the type believed to hold in the full Steinmann hexagon function space.Comment: 70 pages, 3 figures, 4 tables; v2, minor typo corrections and clarification

Heptagons from the Steinmann Cluster Bootstrap

We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar $\mathcal{N} = 4$ supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal ($\bar{Q}$) relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.Comment: 43 pages, 2 figures. v2: typos corrected; version to appear in JHE

Convolution operators supporting hypercyclic algebras

[EN] We show that any convolution operator induced by a non-constant polynomial that vanishes at zero supports a hypercyclic algebra. This partially solves a question raised by R. AronThis work is supported in part by MICINN and FEDER, Project MTM2013-47093-P, and by GVA, Project ACOMP/2015/005.Bès, JP.; Conejero, JA.; Papathanasiou, D. (2017). Convolution operators supporting hypercyclic algebras. Journal of Mathematical Analysis and Applications. 445(2):1232-1238. https://doi.org/10.1016/j.jmaa.2016.01.029S12321238445

The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes

We review the bootstrap method for constructing six- and seven-particle amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, by exploiting their analytic structure. We focus on two recently discovered properties which greatly simplify this construction at symbol and function level, respectively: the extended Steinmann relations, or equivalently cluster adjacency, and the coaction principle. We then demonstrate their power in determining the six-particle amplitude through six and seven loops in the NMHV and MHV sectors respectively, as well as the symbol of the NMHV seven-particle amplitude to four loops.Comment: 36 pages, 4 figures, 5 tables, 1 ancillary file. Contribution to the proceedings of the Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019), 31 August - 25 September 2019, Corfu, Greec

Stability of surfaces in the chalcopyrite system

It has been observed previously that the stable surfaces in chalcopyrites are the polar 112 surfaces. We present an electron microscopy study of epitaxial films of different compositions. It is shown that for both CuGaSe2 and CuInSe2 the 001 surfaces form 112 facets. With increasing Cu excess the faceting is suppressed, indicating a lower surface energy of the 001 surface than the energy of the 112 surface in the Cu rich regime, but the 001 surface is higher in energy than the 112 surface in the Cu poor regime. As both surfaces are polar the stabilization is attributed to defect formatio

An Origin Story for Amplitudes

We classify origin limits of maximally helicity violating multi-gluon scattering amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory, where a large number of cross ratios approach zero, with the help of cluster algebras. By analyzing existing perturbative data, and bootstrapping new data, we provide evidence that the amplitudes become the exponential of a quadratic polynomial in the large logarithms. With additional input from the thermodynamic Bethe ansatz at strong coupling, we conjecture exact expressions for amplitudes with up to 8 gluons in all origin limits. Our expressions are governed by the tilted cusp anomalous dimension evaluated at various values of the tilt angle.Comment: 12 pages, 3 figure

A Novel Algorithm for Nested Summation and Hypergeometric Expansions

We consider a class of sums over products of Z-sums whose arguments differ by a symbolic integer. Such sums appear, for instance, in the expansion of Gauss hypergeometric functions around integer indices that depend on a symbolic parameter. We present a telescopic algorithm for efficiently converting these sums into generalized polylogarithms, Z-sums, and cyclotomic harmonic sums for generic values of this parameter. This algorithm is illustrated by computing the double pentaladder integrals through ten loops, and a family of massive self-energy diagrams through $O(\epsilon^6)$ in dimensional regularization. We also outline the general telescopic strategy of this algorithm, which we anticipate can be applied to other classes of sums.Comment: 36 pages, 2 figures; v2: references added, typos corrected, improved introduction and comparison with existing methods, matches published versio