The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2->5 amplitude in planar N=4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N-particle MHV amplitude in this region to a function, we specialize to N=7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.Comment: 56 pages, 4 figures, 1 table; v2: minor corrections and clarifications, matches published versio

Concept Activation Vectors for Generating User-Defined 3D Shapes

We explore the interpretability of 3D geometric deep learning models in the context of Computer-Aided Design (CAD). The field of parametric CAD can be limited by the difficulty of expressing high-level design concepts in terms of a few numeric parameters. In this paper, we use a deep learning architectures to encode high dimensional 3D shapes into a vectorized latent representation that can be used to describe arbitrary concepts. Specifically, we train a simple auto-encoder to parameterize a dataset of complex shapes. To understand the latent encoded space, we use the idea of Concept Activation Vectors (CAV) to reinterpret the latent space in terms of user-defined concepts. This allows modification of a reference design to exhibit more or fewer characteristics of a chosen concept or group of concepts. We also test the statistical significance of the identified concepts and determine the sensitivity of a physical quantity of interest across the dataset.This is a preprint of the proceeding from S. Druc, A. Balu, P. Wooldridge, A. Krishnamurthy and S. Sarkar, "Concept Activation Vectors for Generating User-Defined 3D Shapes," 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), New Orleans, LA, USA, 2022, pp. 2992-2999, doi: 10.1109/CVPRW56347.2022.00338. Published version © 2022 IEEE. Preprints copyright 2022 The Authors

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

Amplitudes in <i>N</i> = 4 super Yang-Mills: an exploration of kinematical limits

In this thesis we explore aspects of scattering amplitudes in planar N = 4 super Yang-Mills. In particular we shall focus on studying the mathematical structure of scattering amplitudes in different kinematical limits. First we use linear combinations of differential operators and the properties of multiple polylogarithms to solve for a differential equation obeyed by a 2-loop, 5-point dual conformal scalar integral in a coplanar kinematical limit. Next we dedicate the bulk of this thesis to planar amplitudes in multi-Regge kinematics (MRK) and we exploit the simplifications due to this limit to completely classify their mathematical structure.We show that in MRK, the singularity structure of the amplitude corresponds to finite cluster algebras and thus may be described entirely by single-valued multiple polylogarithms. We then present a factorised form for the amplitude expressed as a Fourier-Mellin dispersion integral and proceed to derive novel results at leading logarithmic accuracy (LLA) for both MHV and non-MHV configurations. Specifically we show that amplitudes at L loops are determined by amplitudes with L + 4 legs and classify their leading singularities in MRK. Next we go beyond LLA by using 2-loop, 7-point data to extract corrections to the BFKL central emission vertex which is the only quantity in the dispersion integral not known to all orders. Finally we utilise the corrections to the central emission vertex to conjecture a finite coupling expression and thus extend the dispersion integral for amplitudes in MRK to all orders as well as all multiplicities and helicity configurations

La Camera

We introduce a novel way to perform high-order computations in multi-Regge-kinematics in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory and generalize the existing factorization into building blocks at two loops to all loop orders. Afterwards, we will explain how this framework can be used to easily obtain higher-loop amplitudes from existing amplitudes and how to relate them to amplitudes with higher number of legs.We introduce a novel way to perform high-order computations in multi-Regge-kinematics in planar $\mathcal{N} = 4$ supersymmetric Yang-Mills theory and generalize the existing factorization into building blocks at two loops to all loop orders. Afterwards, we will explain how this framework can be used to easily obtain higher-loop amplitudes from existing amplitudes and how to relate them to amplitudes with higher number of legs

Experiment 2 values for meta d'—d' post TMS minus pre (above threshold results in bold).

<p>Experiment 2 values for meta d'—d' post TMS minus pre (above threshold results in bold).</p

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2->5 amplitude in planar N=4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N-particle MHV amplitude in this region to a function, we specialize to N=7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively

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