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We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…

High Energy Physics - Phenomenology · Physics 2020-11-24 Zeno Capatti , Valentin Hirschi , Dario Kermanschah , Andrea Pelloni , Ben Ruijl

We study 3-point functions at finite temperature in the closed time path formalism. We give a general decomposition of the eight component tensor in terms of seven vertex functions. We derive a spectral representation for these seven…

High Energy Physics - Theory · Physics 2009-10-09 M. E. Carrington , U. Heinz

A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and…

High Energy Physics - Phenomenology · Physics 2009-11-11 Y. Kurihara , T. Kaneko

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…

Number Theory · Mathematics 2025-01-07 Robert Reynolds , Allan Stauffer

We calculate holographically three-point functions of scalar operators with large dimensions at finite density and finite temperature. To achieve this, we construct new solutions that involve two isometries of the deformed internal space.…

High Energy Physics - Theory · Physics 2023-09-15 George Georgiou , Dimitrios Zoakos

Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integrals. However, unless the phase function governing the…

Numerical Analysis · Mathematics 2023-12-07 A. Gibbs , D. P. Hewett , D. Huybrechs

We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to…

Analysis of PDEs · Mathematics 2022-10-18 Raphaël C. Assier , Andrey V. Shanin , Andrey I. Korolkov

A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of…

High Energy Physics - Theory · Physics 2007-05-23 A. I. Davydychev

We study deformations of plane curve singularities from an analytic point of view and obtain some new concrete results. We show some rather unexpected properties of Puiseux coefficients treated as functions on a suitably defined parameter…

Algebraic Geometry · Mathematics 2012-03-20 Maciej Borodzik

We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible, the general idea is first illustrated on the simplest case: a…

Mathematical Physics · Physics 2008-11-26 Klaus Kirsten , Alan McKane

A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…

High Energy Physics - Theory · Physics 2020-12-16 I. A. B. Strachan

This note discusses recent new approaches to studying flopping curves on 3-folds. In a joint paper, the author and Michael Wemyss introduced a 3-fold invariant, the contraction algebra, which may be associated to such curves. It…

Algebraic Geometry · Mathematics 2015-11-06 Will Donovan

We use the holographic methods to calculate the entanglement entropy for field theories modified by $T\bar{T}$ insertion. Based on the available holographic proposals, this calculation reduces to the holographic computations in AdS with…

High Energy Physics - Theory · Physics 2022-01-26 Kuroush Allameh , Amin Faraji Astaneh , Alireza Hassanzadeh

We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integration surface to bypass the integrands' singularities, is…

Analysis of PDEs · Mathematics 2024-05-28 Andrey V. Shanin , Raphael C. Assier , Andrey I. Korolkov , Oleg I. Makarov

This paper considers the open challenge of identifying complete, concise, and explainable quantitative microstructure representations for disordered heterogeneous material systems. Completeness and conciseness have been achieved through…

Materials Science · Physics 2021-09-07 Sheng Cheng , Yang Jiao , Yi Ren

Quasi-primary correlators in two-dimensional conformal field theories deformed simultaneously by $T\bar T$ and root-$T\bar T$ are studied. A path-integral formulation motivated by the geometric realization of the combined deformation is…

High Energy Physics - Theory · Physics 2026-04-17 Bo-Rui Li , Song He , Yu-Xiao Liu

Given the recent progress in computing three-point functions in N=4 SYM via integrability, I provide here a novel direct calculation of some structure constants at weak coupling. The main focus is on correlators involving more than one…

High Energy Physics - Theory · Physics 2019-05-01 Marco S. Bianchi

It is analysed the triple-cut of one-loop amplitudes in dimensional regularisation within spinor-helicity representation. The triple-cut is defined as a difference of two double-cuts with the same particle content, and a same propagator…

High Energy Physics - Theory · Physics 2008-11-26 Pierpaolo Mastrolia

We use Integrability techniques to compute structure constants in N=4 SYM to leading order. Three closed spin chains, which represent the single trace gauge-invariant operators in N=4 SYM, are cut into six open chains which are then sewed…

High Energy Physics - Theory · Physics 2011-09-12 Jorge Escobedo , Nikolay Gromov , Amit Sever , Pedro Vieira

We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be…

High Energy Physics - Phenomenology · Physics 2015-06-12 Sebastian Becker , Stefan Weinzierl