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Related papers: The m=2 amplituhedron

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We obtain compact formulae for tree super-amplitudes for 10 and 11-dimensional supergravity and 10-dimensional supersymmetric Yang-Mills and Born-Infeld. These are based on the \emph{polarised scattering equations}. These incorporate…

High Energy Physics - Theory · Physics 2020-03-11 Yvonne Geyer , Lionel Mason

This article introduces a new approach to implement positivity for the 2-loop n-particle MHV amplituhedron, circumventing the conventional triangulation with respect to positive variables of each cell carved out by the sign flips. This…

High Energy Physics - Theory · Physics 2020-11-06 Ryota Kojima , Junjie Rao

In this paper, we study a new application of the positive Grassmanian to Wilson loop diagrams (or MHV diagrams) for scattering amplitudes in N=4 Super Yang-Mill theory ($N=4$ SYM). There has been much interest in studying this theory via…

Mathematical Physics · Physics 2016-07-20 Susama Agarwala , Eloi Marin Amat

The loop-Amplituhedron $\mathcal{A}^{(L)}_{n}$ is a semialgebraic set in the product of Grassmannians $\mathrm{Gr}_{\mathbb{R}}(2,4)^L$. Recently, many aspects of this geometry for the case of $L=1$ have been elucidated, such as its…

High Energy Physics - Theory · Physics 2026-04-08 Gabriele Dian , Elia Mazzucchelli , Felix Tellander

Taking the N=2 strings as the starting point, we discuss the equivalent self-dual field theories and analyse their symmetry structure in 2+2 dimensions. Restoring the full `Lorentz' invariance in the target space necessarily leads to an…

High Energy Physics - Theory · Physics 2009-10-30 Sergei V. Ketov

The geometric structure of S-matrix encapsulated by the "Amplituhedron program" has begun to reveal itself even in non-supersymmetric quantum field theories. Starting with the seminal work of Arkani-Hamed, Bai, He and Yan it is now…

High Energy Physics - Theory · Physics 2022-05-04 Mrunmay Jagadale , Alok Laddha

Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called…

High Energy Physics - Theory · Physics 2020-10-28 Tomasz Lukowski , Robert Moerman

We study a novel geometric expansion for scattering amplitudes in the planar sector of N=4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive…

High Energy Physics - Theory · Physics 2024-01-01 Taro V. Brown , Umut Oktem , Shruti Paranjape , Jaroslav Trnka

In this paper, we present new expressions for n-point NMHV tree-level gravity amplitudes. We introduce a method of factorization diagrams which is a simple graphical representation of R-invariants in Yang-Mills theory. We define the gravity…

High Energy Physics - Theory · Physics 2021-05-12 Jaroslav Trnka

In this note we make a field-theoretical derivation of a series of new recursion relations by a one-parameter deformation of kinematic variables for tree and one-loop amplitudes of bi-adjoint $\phi^3$ theory. Tree amplitudes are given by…

High Energy Physics - Theory · Physics 2020-10-26 Qinglin Yang

A central problem in quantum field theory is the computation of scattering amplitudes. However, traditional methods are impractical to calculate high order phenomenologically relevant observables. Building on a few decades of astonishing…

High Energy Physics - Theory · Physics 2017-06-28 Livia Ferro , Tomasz Lukowski , Andrea Orta , Matteo Parisi

Following the spirit of S-matrix program, we proposed a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified…

High Energy Physics - Theory · Physics 2015-05-20 Jia-Hui Huang , Rijun Huang , Yin Jia

It is known for ten years that self-dual Yang-Mills theory is the effective field theory of the open N=2 string in 2+2 dimensional spacetime. We uncover an infinite set of abelian rigid string symmetries, corresponding to the symmetries and…

High Energy Physics - Theory · Physics 2015-06-25 Tatiana A. Ivanova , Olaf Lechtenfeld

We define and study the face stratification of the m=2 amplituhedron. We show that the face poset is an upper order ideal in the face poset of the totally nonnegative Grassmannian. Our construction is consistent with earlier work of…

Combinatorics · Mathematics 2025-05-06 Thomas Lam

In this paper, we define the momentum amplituhedron in the four-dimensional split-signature space of dual momenta. It encodes scattering amplitudes at tree level and loop integrands for N=4 super Yang-Mills in the planar sector. In this…

High Energy Physics - Theory · Physics 2023-08-07 Livia Ferro , Ross Glew , Tomasz Lukowski , Jonah Stalknecht

The amplituhedron is a semialgebraic set given as the image of the non-negative Grassmannian under a linear map subject to a choice of additional parameters. We define the limit amplituhedron as the limit of amplituhedra by sending one of…

Algebraic Geometry · Mathematics 2025-01-15 Joris Koefler , Rainer Sinn

We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we call upper…

Rings and Algebras · Mathematics 2011-11-28 Jorge A. Guccione , Juan J. Guccione , Christian Valqui

We propose a three dimensional non-supersymmetric theory that is conformal in the large N limit. In a certain well defined bosonic sub-sector of gauge invariant operators, this theory is planar equivalent to the theory recently proposed by…

High Energy Physics - Theory · Physics 2008-11-26 Adi Armoni , Asad Naqvi

In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We explain the connection to on-shell…

High Energy Physics - Theory · Physics 2018-05-17 Igor Prlina , Marcus Spradlin , James Stankowicz , Stefan Stanojevic

The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron…

High Energy Physics - Theory · Physics 2020-08-26 Livia Ferro , Tomasz Lukowski , Robert Moerman