4.8 Article

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations

Journal

PHYSICAL REVIEW LETTERS
Volume 117, Issue 24, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.117.241601

Keywords

-

Funding

  1. Danish National Research Foundation [DNRF91]
  2. US Department of Energy [DE-AC02-76SF00515]
  3. Perimeter Institute for Theoretical Physics
  4. Government of Canada through the Department of Innovation, Science and Economic Development Canada
  5. Province of Ontario through the Ministry of Research, Innovation and Science
  6. National Science Foundation [NSF PHY11-25915]

Ask authors/readers for more resources

The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.8
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

Article Physics, Particles & Fields

Cuts and isogenies

Hjalte Frellesvig, Cristian Vergu, Matthias Volk, Matt von Hippel

Summary: The study focuses on genus-one curves that appear in Feynman integrals, analyzing their invariants through various methods and finding consistent geometry across different cases. This supports the notion that there exists an invariant concept of genus-one geometry independent of the computation method. The study also offers insights on interpreting previous results related to isogenies of these curves.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Article Physics, Particles & Fields

N3LO gravitational quadratic-in-spin interactions at G4

Michele Levi, Andrew J. McLeod, Matthew von Hippel

Summary: This study for the first time computes the (NLO)-L-3 gravitational quadratic-in-spin interactions at G(4) in the post-Newtonian (PN) expansion via the effective field theory (EFT) of gravitating spinning objects. The result contributes at the 5PN order for maximally-spinning compact objects, adding the spinning case to the static sector at this PN accuracy. The study requires extending the EFT of a spinning particle beyond linear order in the curvature to include higher-order operators quadratic in the curvature that are relevant at this PN order.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

Article Physics, Multidisciplinary

Folding Amplitudes into Form Factors: An Antipodal Duality

Lance J. Dixon, Omer Gurdogan, Andrew J. McLeod, Matthias Wilhelm

Summary: We observe and provide evidence for the duality between the three-gluon form factor of the chiral part of the stress-tensor multiplet and the six-gluon MHV amplitude in planar N = 4 super-Yang-Mills theory.

PHYSICAL REVIEW LETTERS (2022)

Review Physics, Multidisciplinary

The SAGEX review on scattering amplitudes*

Gabriele Travaglini, Andreas Brandhuber, Patrick Dorey, Tristan McLoughlin, Samuel Abreu, Zvi Bern, N. Emil J. Bjerrum-Bohr, Johannes Bluemlein, Ruth Britto, John Joseph M. Carrasco, Dmitry Chicherin, Marco Chiodaroli, Poul H. Damgaard, Vittorio Del Duca, Lance J. Dixon, Daniele Dorigoni, Claude Duhr, Yvonne Geyer, Michael B. Green, Enrico Herrmann, Paul Heslop, Henrik Johansson, Gregory P. Korchemsky, David A. Kosower, Lionel Mason, Ricardo Monteiro, Donal O'Connell, Georgios Papathanasiou, Ludovic Plante, Jan Plefka, Andrea Puhm, Ana-Maria Raclariu, Radu Roiban, Carsten Schneider, Jaroslav Trnka, Pierre Vanhove, Congkao Wen, Chris D. White

Summary: This is an introduction to a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory, aiming to provide an overview of the field from basic aspects to current research and developments in 2022.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2022)

Review Physics, Multidisciplinary

The SAGEX review on scattering amplitudes Chapter 15: The multi-Regge limit

Vittorio Del Duca, Lance J. Dixon

Summary: This article reviews the Regge and multi-Regge limit of scattering amplitudes in gauge theory, with a focus on QCD and planar N=4 super-Yang-Mills theory. The large logarithms that arise in these limits are identified, and the progress towards resumming them, including next-to-next-to-leading logarithms for BFKL evolution in QCD and all-orders proposals in planar N=4 super-Yang-Mills theory, as well as the perturbative checks of those proposals, is discussed. The application of single-valued multiple polylogarithms to this important kinematical limit of particle scattering is also covered.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2022)

Article Physics, Particles & Fields

Bootstrapping a stress-tensor form factor through eight loops

Lance J. Dixon, Omer Gurdogan, Andrew J. McLeod, Matthias Wilhelm

Summary: In this paper, we compute the three-point form factor of the chiral stress-tensor multiplet in planar N = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops. We bootstrap the computation using boundary data from the form factor operator product expansion. By observing and employing new restrictions on pairs and triples of adjacent letters in the symbol, we obtain detailed information about the function space required to describe the form factor through eight loops. The numerical results provide strong evidence for a finite radius of convergence of perturbation theory. Our results are expected to give the highest weight part of the gg -> Hg and H -> ggg amplitudes in the heavy-top limit of QCD through eight loops. They also contribute to the recent discovery of a new antipodal duality between this form factor and a six-point amplitude in the same theory.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Article Physics, Particles & Fields

One-loop central-emission vertex for two gluons in N=4 super Yang-Mills theory

Emmet P. Byrne, Vittorio Del Duca, Lance J. Dixon, Einan Gardi, Jennifer M. Smillie

Summary: This study addresses the one-loop contribution of the two-gluon CEV in N=4 super Yang-Mills theory and finds that its dispersive part can be factorized into two-gluon CEVs. Although computed in a specific limit, these results capture the complexity of six-gluon amplitudes in general cases.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

Article Physics, Multidisciplinary

All-Orders Quadratic-Logarithmic Behavior for Amplitudes

Benjamin Basso, Lance J. Dixon, Yu-Ting Liu, Georgios Papathanasiou

Summary: We use cluster algebras to classify the origin limits of maximally helicity violating multigluon scattering amplitudes in planar N = 4 super-Yang-Mills theory. By analyzing perturbative data and bootstrapping new data, we find evidence that the amplitudes become the exponential of a quadratic polynomial in the large logarithms. With input from the thermodynamic Bethe ansatz at strong coupling, we propose exact expressions for amplitudes with up to eight gluons in all origin limits, which are governed by the tilted cusp anomalous dimension evaluated at various tilt angles.

PHYSICAL REVIEW LETTERS (2023)

Article Physics, Multidisciplinary

Antipodal Self-Duality for a Four-Particle Form Factor

Lance J. Dixon, Oemer Guerdogan, Yu -Ting Liu, Andrew J. McLeod, Matthias Wilhelm

Summary: We derive the symbol of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar N = 4 super-Yang-Mills theory at two loops. The symbol involves only 34 letters and satisfies the extended Steinmann relations in all partially overlapping three-particle momentum channels. Furthermore, the remainder function for this form factor exhibits an antipodal self-duality that holds on a four-dimensional parity-preserving kinematic hypersurface. This self-duality implies the recently noticed antipodal duality between the three-particle form factor and the six-particle amplitude in this theory.

PHYSICAL REVIEW LETTERS (2023)

Article Physics, Particles & Fields

An eight loop amplitude via antipodal duality

Lance J. Dixon, Yu-Ting Liu

Summary: This paper calculates the six-particle maximally-helicity-violating (MHV) amplitude in planar N = 4 super-Yang-Mills theory at eight loops using antipodal duality and the recently computed eight-loop three-point form factor. Antipodal duality maps the form factor symbol to the amplitude symbol on a two-dimensional parity-preserving surface. The amplitude successfully passes various tests, validating the usage of antipodal duality at eight loops.

JOURNAL OF HIGH ENERGY PHYSICS (2023)

Article Physics, Multidisciplinary

A symbol and coaction for higher-loop sunrise integrals

Andreas Forum, Matt von Hippel

Summary: We have constructed a symbol and coaction for the l-loop sunrise family of integrals, both for equal-mass and generic-mass cases. These examples are the first concrete instances of symbols and coactions for integrals involving Calabi-Yau threefolds and higher. We have recast the differential equations satisfied by these integrals into a unipotent form in order to obtain a symbol of finite length. We have also augmented the integrals by including ratios of maximal cuts and tau;i in a natural way. We discuss the connection of this construction to symbols and coactions for multiple polylogarithms, elliptic multiple polylogarithms, and notions of transcendental weight.

SCIPOST PHYSICS CORE (2023)

Article Astronomy & Astrophysics

Implications of the Landau equations for iterated integrals

Holmfridur S. Hannesdottir, Andrew J. McLeod, Matthew D. Schwartz, Cristian Vergu

Summary: We introduce a method to derive constraints on the symbol of Feynman integrals by analyzing their asymptotic expansions near Landau loci. We illustrate this method on integrals with generic masses and prove a conjectured bound on the transcendental weight of polylogarithmic l-loop integrals. Additionally, we derive new constraints on the kinematic dependence of certain products of symbol letters near singular points.

PHYSICAL REVIEW D (2022)

Article Physics, Particles & Fields

Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics

Lance J. Dixon, Yu-Ting Liu, Julian Miczajka

Summary: This paper computes all 2 -> 5 gluon scattering amplitudes in planar N = 4 super-Yang-Mills theory in the multi-Regge limit. The results are provided through four loops and to all logarithmic accuracy at leading power, represented in terms of single-valued multiple polylogarithms of two variables. By leveraging function-level results in the Steinmann cluster bootstrap, the authors find agreement with the recently conjectured all-order central emission vertex, providing a resummation of Fourier-Mellin residues into single-valued polylogarithms and an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.

JOURNAL OF HIGH ENERGY PHYSICS (2021)

No Data Available