☆ 4.4 Article

Unwinding the amplituhedron in binary

JOURNAL OF HIGH ENERGY PHYSICS (2018)

Journal

JOURNAL OF HIGH ENERGY PHYSICS

Volume -, Issue 1, Pages -

Publisher

SPRINGER

DOI: 10.1007/JHEP01(2018)016

Keywords

Scattering Amplitudes; Supersymmetric Gauge Theory

Categories

Physics, Particles & Fields

Funding

DOE [DOE DE-SC0009988]
NSERC
Canada Research Chairs program

Ask authors/readers for more resources

Protocol

Community support

Reagent

Community support

Abstract

We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting con figuration of points has a specified (and maximal) generalized winding number. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of sign flips of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural dual of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the con figuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.

Authors

I am an author on this paper

Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.4

Not enough ratings

Secondary Ratings

Novelty

-

Significance

-

Scientific rigor

-

Rate this paper

Recommended

Article Physics, Particles & Fields

Sequential discontinuities of Feynman integrals and the monodromy group

Jacob L. Bourjaily, Holmfridur Hannesdottir, Andrew J. McLeod, Matthew D. Schwartz, Cristian Vergu

Summary: In this study, we extend the relationship between discontinuities of scattering amplitudes and cut diagrams to include sequential discontinuities in arbitrary momentum channels. The new relations, derived using time-ordered perturbation theory, hold at phase-space points where all cut momentum channels are simultaneously accessible. As part of the analysis, the computation of sequential discontinuities as monodromies is explained, with the use of the monodromy group explored in characterizing the analytic properties of Feynman integrals. Multiple cross-checks of the new formulas are performed in polylogarithmic examples, sometimes extending to all loop orders.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron

Song He, Chia-Kai Kuo, Zhenjie Li, Yao-Qi Zhang

Summary: In this study, we extensively investigate a recently proposed new positive geometry, which is conjectured to be the four-point amplituhedron for ABJM theory. We examine generalized unitarity cuts from this geometry, and demonstrate that (1) the four-point integrand satisfies perturbative unitarity (or optical theorem) at all loops, a result that directly follows from the geometry, and (2) vanishing cuts involving odd-point amplitudes arise from the bipartite nature of the associated negative geometries, providing justification for their presence in ABJM theory. Additionally, we make progress in integrating the forms of these negative geometries and obtain an infrared-finite quantity up to two loops, allowing us to extract the cusp anomalous dimension at leading order.

JOURNAL OF HIGH ENERGY PHYSICS (2023)

Add to Collection

Article Physics, Particles & Fields

Poles at infinity in on-shell diagrams

Taro V. Brown, Umut Oktem, Jaroslav Trnka

Summary: In this paper, we investigate the on-shell diagrams in N < 4 supersymmetric Yang-Mills theory. These diagrams are gauge invariant objects that appear as cuts of loop integrands and serve as building blocks for amplitudes. We show that there are new UV poles in on-shell diagrams of N < 4 SYM theories when the loop momenta go to infinity, which can be interpreted as a diagrammatic operation involving pinching a loop and performing a non-planar twist on external legs.

JOURNAL OF HIGH ENERGY PHYSICS (2023)

Add to Collection

Article Physics, Particles & Fields

On the geometry of the orthogonal momentum amplituhedron

Tomasz Lukowski, Robert Moerman, Jonah Stalknecht

Summary: Hypochlorite (ClO-) is an important component of reactive oxygen species (ROS) and plays a crucial role in biological systems. Hypochlorous acid (HOCl) is a powerful antimicrobial agent, but excessive HOCl formation can lead to tissue diseases. Therefore, monitoring ClO- concentration and studying its distribution in living cells are of great importance in cell biology and medical diagnosis.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Add to Collection

Article Physics, Particles & Fields

The momentum amplituhedron of SYM and ABJM from twistor-string maps

Song He, Chia-Kai Kuo, Yao-Qi Zhang

Summary: This study investigates the connection between twistor-string formulas for tree amplitudes in N = 4 SYM and N = 6 ABJM and the corresponding momentum amplituhedron in D = 4 and D = 3 kinematic spaces. The authors propose twistor-string maps from different Grassmannians to the kinematic spaces and provide strong evidence that these maps are diffeomorphisms. They also show how boundaries of certain moduli spaces map to boundaries of momentum amplituhedra, excluding unwanted channels.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Add to Collection

Article Physics, Particles & Fields

Comments on all-loop constraints for scattering amplitudes and Feynman integrals

Song He, Zhenjie Li, Qinglin Yang

Summary: We comment on the status of Steinmann-like constraints and summarize their application to the symbols of scattering amplitudes and Feynman integrals in planar N = 4 super-Yang-Mills. We find that extended-Steinmann relations hold for various finite integrals and MHV amplitudes, with interesting cancellation between rational and algebraic letters. Additionally, we propose a list of possible last-two-entries for MHV amplitudes up to 9 points derived from (Q) over bar equations.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Add to Collection

Article Physics, Particles & Fields

Hexagon bootstrap in the double scaling limit

Vsevolod Chestnov, Georgios Papathanasiou

Summary: The study focuses on the six-particle amplitude in planar N = 4 super Yang-Mills theory in the double scaling (DS) limit, constructing the relevant function space and computing the non-divergent coefficient of a certain component of the amplitude. Results are also specialized to the overlapping origin limit, observing a general pattern for its leading divergences.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

Symbol alphabets from plabic graphs III: n=9

J. Mago, A. Schreiber, M. Spradlin, A. Yelleshpur Srikant, A. Volovich

Summary: In this paper, we study the symbol alphabets of n-particle amplitudes in N = 4 super-Yang-Mills theory, solving the CZ = 0 matrix equations associated with the totally non-negative Grassmannian using methods from previous works. We identify sets of parameterizations that produce solutions for specific cells and determine the origins of algebraic letters through plabic graphs.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

The two-loop remainder function for eight and nine particles

John Golden, Andrew J. McLeod

Summary: The paper utilizes the cluster-algebraic structure to upgrade the symbols of two-loop MHV amplitudes in planar N = 4 supersymmetric Yang Mills theory to complete analytic functions. By systematically projecting and matching components to multiple polylogarithms with negative cluster-coordinate arguments, the additive constant is determined analytically. The unique decomposition of the nonclassical part of each amplitude in terms of a specific A(3) cluster polylogarithm is observed, along with the exploration of the numerical behavior of the remainder function.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

Celestial dual superconformal symmetry, MHV amplitudes and differential equations

Yangrui Hu, Lecheng Ren, Akshay Yelleshpur Srikant, Anastasia Volovich

Summary: This paper explores the celestial avatar of dual superconformal symmetry in N = 4 Yang-Mills theory and identifies the corresponding relationship between celestial amplitudes and momentum space amplitudes.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

The Grassmannian for celestial superamplitudes

Livia Ferro, Robert Moerman

Summary: This paper investigates tree-level scattering amplitudes in N=4 super Yang-Mills theory and presents a Grassmannian formulation of their celestial counterparts. This opens up a path towards a geometric picture for celestial superamplitudes, inspired by positive geometries.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

Momentum amplituhedron meets kinematic associahedron

David Damgaard, Livia Ferro, Tomasz Lukowski, Robert Moerman

Summary: This paper studies the relationship between the momentum amplituhedron and the kinematic associahedron, finding a direct link between them in four-dimensional spacetime. The analysis highlights the common singularity structure of their amplitudes.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Add to Collection

Article Physics, Particles & Fields

Integrated negative geometries in ABJM

Johannes M. M. Henn, Martin Lagares, Shun-Qing Zhang

Summary: In this study, we investigate the infrared-finite functions obtained from integrating the logarithm of the four-particle scattering amplitude over L - 1 loops in the three-dimensional N = 6 Chern-Simonsmatter (ABJM) theory. By organizing the integrands using negative geometries, we ensure that the integrals do not diverge if at least one loop variable is left unintegrated. We explicitly perform the integrations up to L = 3 and find both parity-even and-odd terms. Additionally, we propose a prescription to compute the cusp anomalous dimension Gcusp of ABJM using the integrated negative geometries and successfully reproduce its first non-trivial order. Finally, we demonstrate that the leading singularities in the integrated results are conformally invariant.

JOURNAL OF HIGH ENERGY PHYSICS (2023)

Add to Collection

Article Physics, Particles & Fields

A study of Feynman integrals with uniform transcendental weights and their symbology

Song He, Zhenjie Li, Rourou Ma, Zihao Wu, Qinglin Yang, Yang Zhang

Summary: This paper derives two-loop four-external-mass Feynman integrals with uniform transcendental weights based on recent developments, and explores the relationship between symbol structures and certain dual conformal integrals.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Add to Collection

Article Physics, Particles & Fields

Full-color three-loop three-point form factors in N=4 SYM

Guanda Lin, Gang Yang, Siyuan Zhang

Summary: We present the detailed computation of full-color three-loop three-point form factors in N = 4 SYM using the color-kinematics duality and generalized unitarity method. The numerical evaluation shows that the computations can be simplified by expressing the integrals in terms of uniformly transcendental basis.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Add to Collection

No Data Available

No Data Available

© Peeref 2019-2024. All rights reserved.