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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…

High Energy Physics - Phenomenology · Physics 2014-11-20 Vittorio Del Duca , Claude Duhr , Vladimir A. Smirnov

An effective action is proposed to compute the expectation value of Wilson loops in $(S)U(N)$ gauge theories. The action consists of fermions localized on the loop and an Abelian gauge field that fixes the representation. The discussion is…

High Energy Physics - Theory · Physics 2018-08-01 Carlos Hoyos

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…

Numerical Analysis · Mathematics 2020-06-11 Yousef Saad , Mohamed El-Guide , Agnieszka Międlar

We derive a system of differential equations which are satisfied by the vevs of BPS Wilson loops and 't Hooft coupling of ABJM theory. They are Picard-Fuchs equations of an algebraic curve defined by the derivative of the planar resolvent…

High Energy Physics - Theory · Physics 2025-09-23 Takao Suyama

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in…

High Energy Physics - Theory · Physics 2017-06-28 Jacob L. Bourjaily , Enrico Herrmann , Jaroslav Trnka

We consider the vacuum expectation values of 1/2-BPS circular Wilson loops in N=4 super Yang-Mills theory in the totally antisymmetric representation of the gauge group U(N) or SU(N). Localization and matrix model techniques provide exact,…

High Energy Physics - Theory · Physics 2018-08-29 Anthonny F. Canazas Garay , Alberto Faraggi , Wolfgang Mück

We consider 4-dimensional $\mathcal{N} = 2$ superconformal quiver theories with $SU(N)^M$ gauge group and bi-fundamental matter and we evaluate correlation functions of $n$ coincident Wilson loops in the planar limit of the theory.…

High Energy Physics - Theory · Physics 2023-12-06 Alessandro Pini , Paolo Vallarino

In this paper we study Wilson loops in various representations for finite and large values of the color gauge group for supersymmetric ${\cal N}=4$ gauge theories. We also compute correlators of Wilson loops in different representations and…

High Energy Physics - Theory · Physics 2018-11-14 Ekaterina Sysoeva

We investigate the matching of eigenvalue densities of Wilson loops in SU(N) lattice gauge theory: the eigenvalue densities in 1+1, 2+1 and 3+1 dimensions are nearly identical when the traces of the loops are equal. We show that the…

High Energy Physics - Theory · Physics 2008-11-26 Francis Bursa

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary…

High Energy Physics - Theory · Physics 2015-05-30 Hugo Reinhardt , Markus Quandt , Giuseppe Burgio

The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…

High Energy Physics - Theory · Physics 2011-10-19 Janusz Gluza , Krzysztof Kajda , David A. Kosower

A finite expansion of the exponential map for a $N\times N$ matrix is presented. The method uses the Cayley-Hamilton theorem for writing the higher matrix powers in terms of the first N-1 ones. The resulting sums over the corresponding…

High Energy Physics - Theory · Physics 2008-11-26 Alexander Laufer

We compute the circular Wilson loop of N=4 SYM theory at large N in the rank k symmetric and antisymmetric tensor representations. Using a quadratic Hermitian matrix model we obtain expressions for all values of the 't Hooft coupling. At…

High Energy Physics - Theory · Physics 2011-04-15 Sean A. Hartnoll , S. Prem Kumar

We show how studying leading singularities of Feynman diagrams, when all momenta are complex, gives a simple way of writing multi-loop and multi-particle scattering amplitudes in N=4 super Yang-Mills. The simplicity of the method is…

High Energy Physics - Theory · Physics 2008-03-14 Freddy Cachazo

The scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for formulae at one loop on a torus for 10 dimensional…

High Energy Physics - Theory · Physics 2016-04-20 Yvonne Geyer , Lionel Mason , Ricardo Monteiro , Piotr Tourkine

We investigate the consequences of elliptic leading singularities for the unitarity-based representations of two-loop amplitudes in planar, maximally supersymmetric Yang-Mills theory. We show that diagonalizing with respect to these leading…

High Energy Physics - Theory · Physics 2021-12-22 Jacob L. Bourjaily , Nikhil Kalyanapuram , Cameron Langer , Kokkimidis Patatoukos

We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with…

High Energy Physics - Theory · Physics 2011-07-19 Simon Caron-Huot

We study the circular Wilson loop in the symmetric representation of U(N) in $\mathcal{N} = 4$ super-Yang-Mills (SYM). In the large N limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests…

High Energy Physics - Theory · Physics 2017-01-11 Xinyi Chen-Lin

This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…

Numerical Analysis · Mathematics 2013-06-24 Michael Karow , Emre Mengi

In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…

Statistics Theory · Mathematics 2024-05-09 Piotr Zwiernik