An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM

In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry constrains multi-loop n-edged Wilson loops to be basically given in terms of the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a function of conformally invariant cross ratios. We identify a class of kinematics for which the Wilson loop exhibits exact Regge factorisation and which leave invariant the analytic form of the multi-loop n-edged Wilson loop. In those kinematics, the analytic result for the Wilson loop is the same as in general kinematics, although the computation is remarkably simplified with respect to general kinematics. Using the simplest of those kinematics, we have performed the first analytic computation of the two-loop six-edged Wilson loop in general kinematics.Comment: 17 pages. Extended discussion on how the QMRK limit is taken. Version accepted by JHEP. A text file containing the Mathematica code with the analytic expression for the 6-point remainder function is include

Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders

Scattering amplitudes of partons in QCD contain infrared divergences which can be resummed to all orders in terms of an anomalous dimension. Independently, in the limit of high-energy forward scattering, large logarithms of the energy can be resummed using Balitsky-Fadin-Kuraev-Lipatov theory. We use the latter to analyze the infrared-singular part of amplitudes to all orders in perturbation theory and to next-to-leading-logarithm accuracy in the high-energy limit, resumming the two-Reggeon contribution. Remarkably, we find a closed form for the infrared-singular part, predicting the Regge limit of the soft anomalous dimension to any loop order.Comment: 35 pages, 8 figure

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.Comment: 104 pages, six awesome figures and ancillary files containing the results in Mathematica forma

Bootstrapping the three-loop hexagon

We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N=4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3-->3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.Comment: 36 pages, 1 figure, plus 8 ancillary files containing symbols of functions; v2 minor typo correction

The infrared structure of gauge theory amplitudes in the high-energy limit

We develop an approach to the high-energy limit of gauge theories based on the universal properties of their infrared singularities. Our main tool is the dipole formula, a compact ansatz for the all-order infrared singularity structure of scattering amplitudes of massless partons. By taking the high-energy limit, we show that the dipole formula implies Reggeization of infrared-singular contributions to the amplitude, at leading logarithmic accuracy, for the exchange of arbitrary color representations in the cross channel. We observe that the real part of the amplitude Reggeizes also at next-to-leading logarithmic order, and we compute the singular part of the two-loop Regge trajectory, which is universally expressed in terms of the cusp anomalous dimension. Our approach provides tools to study the high-energy limit beyond the boundaries of Regge factorization: thus we show that Reggeization generically breaks down at next-to-next-to-leading logarithmic accuracy, and provide a general expression for the leading Reggeization-breaking operator. Our approach applies to multiparticle amplitudes in multi-Regge kinematics, and it also implies new constraints on possible corrections to the dipole formula, based on the Regge limit

The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory

We consider the multi-Regge limit for N=4 SYM NMHV leading color amplitudes in two different formulations: the BFKL formalism for multi-Regge amplitudes in leading logarithm approximation, and superconformal N=4 SYM amplitudes. It is shown that the two approaches agree to two-loops for the 2->4 and 3->3 six-point amplitudes. Predictions are made for the multi-Regge limit of three loop 2->4 and 3->3 NMHV amplitudes, as well as a particular sub-set of two loop 2 ->2 +n N^kMHV amplitudes in the multi-Regge limit in the leading logarithm approximation from the BFKL point of view.Comment: 28 pages, 3 figure

Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3

We study classical open string solutions with a null polygonal boundary in AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS_n and generalized parafermions.Comment: 25 pages, 4 figures, v2: a figure and references added, minor corrections, v3: references added, minor corrections, to appear in JHE

FAIR environmental and health registry (FAIREHR)- supporting the science to policy interface and life science research, development and innovation

The environmental impact on health is an inevitable by-product of human activity. Environmental health sciences is a multidisciplinary field addressing complex issues on how people are exposed to hazardous chemicals that can potentially affect adversely the health of present and future generations. Exposure sciences and environmental epidemiology are becoming increasingly data-driven and their efficiency and effectiveness can significantly improve by implementing the FAIR (findable, accessible, interoperable, reusable) principles for scientific data management and stewardship. This will enable data integration, interoperability and (re)use while also facilitating the use of new and powerful analytical tools such as artificial intelligence and machine learning in the benefit of public health policy, and research, development and innovation (RDI). Early research planning is critical to ensuring data is FAIR at the outset. This entails a well-informed and planned strategy concerning the identification of appropriate data and metadata to be gathered, along with established procedures for their collection, documentation, and management. Furthermore, suitable approaches must be implemented to evaluate and ensure the quality of the data. Therefore, the 'Europe Regional Chapter of the International Society of Exposure Science' (ISES Europe) human biomonitoring working group (ISES Europe HBM WG) proposes the development of a FAIR Environment and health registry (FAIREHR) (hereafter FAIREHR). FAIR Environment and health registry offers preregistration of studies on exposure sciences and environmental epidemiology using HBM (as a starting point) across all areas of environmental and occupational health globally. The registry is proposed to receive a dedicated web-based interface, to be electronically searchable and to be available to all relevant data providers, users and stakeholders. Planned Human biomonitoring studies would ideally be registered before formal recruitment of study participants. The resulting FAIREHR would contain public records of metadata such as study design, data management, an audit trail of major changes to planned methods, details of when the study will be completed, and links to resulting publications and data repositories when provided by the authors. The FAIREHR would function as an integrated platform designed to cater to the needs of scientists, companies, publishers, and policymakers by providing user-friendly features. The implementation of FAIREHR is expected to yield significant benefits in terms of enabling more effective utilization of human biomonitoring (HBM) data.Most co-authors were financialy supported with their respective inistitution. Some of the co-authors were financialy supportrd by the Safe and Efficient Chemistry by Design (SafeChem) project (grant no. DIA 2018/11) funded by the Swedish Foundation for Strategic Environmental Research, and by the PARC project (grant no. 101057014) funded under the European Union's Horizon Europe Research and Innovation program