Gluons and gravitons at one loop from ambitwistor strings

Self Cite

We propose new formulae for the two-loop n-point D-dimensional integrands of scattering amplitudes in Yang-Mills theory and gravity. The loop integrands are written as a double-forward limit of tree-level trivalent diagrams, and are inferred from the formalism of the two-loop scattering equations. We discuss the relationship between the formulae for non-supersymmetric theories and the Neveu-Schwarz sector of the formulae for maximally supersymmetric theories, which can be derived from ambitwistor strings. An important property of the loop integrands is that they are expressed in a representation that includes linear-type propagators. This representation exhibits a loop-level version of the colour-kinematics duality, which follows directly from tree level via the double-forward limit. arXiv:1908.05221v1 [hep-th] Contents 6 Conclusion 32 A Two-loop partition functions and propagators on the Riemann sphere 33 A.1 Two-loop partition functions 33 A.2 Two-loop propagators 341 IntroductionWorldsheet techniques inspired by string theory offer an alternative to the Feynman diagram approach for calculating scattering amplitudes in quantum field theory, in particular for theories of massless particles. This broad programme has seen remarkable advances in recent years. Our aims are to extend the lessons learned at tree level and one loop to two-loop amplitudes, and to interpret previous two-loop results for maximally supersymmetric theories in a more general context, allowing for reduced or no supersymmetry. Even though we will motivate our proposal for two-loop amplitudes from the insights of this 'stringy' approach, the proposal itself will not be written in a worldsheet language. It will instead be written in a (non-Feynman) diagrammatic language, whereby the two-loop integrands are suitably defined double-forward limits of tree-level amplitudes. The worldsheet techniques that inspire our work originated in Witten's twistor string [1] describing four-dimensional super-Yang-Mills theory, and in the corresponding 'connected prescription' to compute scattering amplitudes [2]. In this approach, tree-level scattering amplitudes for n massless particles are computed as integrals over the moduli space of punctured Riemann spheres, M 0,n . The -1 -modern version of these advances, applicable to theories of massless particles in any number of dimensions, was developed by Cachazo, He and Yuan (CHY) [3][4][5], who discovered the general type of formulae, and by Mason and Skinner [6], who constructed the associated type of worldsheet model; the ambitwistor string. For a variety of interesting theories in this framework, see e.g. [7,8]. The ambitwistor string models reproducing Yang-Mills and gravity amplitudes are supersymmetric, but the extraction of amplitudes in non-supersymmetric theories is possible even at loop level, as we shall discuss. For a comparison of the bosonic and supersymmetric ambitwistor strings, see [9,10]. For recent work on moduli-space formulae tuned to a specific number of spacetime dimensions using the spinor...

Section: Checks On Maximal Unitarity Cutsmentioning

confidence: 99%

“…We will build on work at one loop [18,71], where a different version of the loop-level colourkinematics duality was described. This version is adapted to the type of representation of the loop integrand that we alluded to previously, which includes non-Feynman propagators.…”

mentioning

confidence: 99%

Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality

Geyer

Monteiro

Stark-Muchão

2019

Self Cite

“…interplay of GEIs with the color-kinematics dual field-theory amplitudes obtained from the methods of [51,52]. The same questions will arise at higher genus [53,54].…”

Section: Discussionmentioning

confidence: 86%

Towards the n-point one-loop superstring amplitude. Part III. One-loop correlators and their double-copy structure

Mafra

Schlotterer

2019

In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued. A key driving force in this construction is the generalization of a so far unnoticed property at tree level; the correlators have the symmetry structure akin to Lie polynomials. One-loop correlators up to seven points are presented in a variety of representations manifesting different subsets of their defining properties. These expressions are related via identities obeyed by the kinematic superfields and worldsheet functions spelled out in the first two parts of this series and reflecting a duality between the two kinds of ingredients.Interestingly, the expression for the eight-point correlator following from our method seems to capture correctly all the dependence on the worldsheet punctures but leaves undetermined the coefficient of the holomorphic Eisenstein series G 4 . By virtue of chiral splitting, closed-string correlators follow from the double copy of the open-string results.December 2018 †

“…A clear limitation of the 4D scattering equations is that they currently only support tree-level calculations, and an obvious future direction is to investigate calculation of looplevel integrands using these methods. Loop-level scattering equations exist in general dimensions [50,51], and future work could implement numerical algorithms to evaluate loop-level integrands as sums over solutions to the general d equations.…”

Section: Discussionmentioning

confidence: 99%

A Monte Carlo approach to the 4D scattering equations

Farrow

2018

Abstract:The scattering equation formalism is a general framework for calculation of amplitudes in theories of massless particles. We provide a detailed introduction to the 4D scattering equation framework accessible to non-experts, outline current difficulties solving the equations numerically, and explain how to overcome them with a Monte Carlo algorithm. With this submission we include treeamps4dJAF, the first publicly available Mathematica package for calculating amplitudes by solving the scattering equations, supporting MHV analytical and N k−2 MHV numerical computations. The package provides a powerful and flexible computational tool for calculating tree-level amplitudes in super Yang Mills theories, Einstein supergravity and conformal supergravity. We tabulate sets of numerical solutions up to 9 points in all MHV sectors and 12 points in the NHMV sector which can be used for fast evaluation of amplitudes.