New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

He, Song; Schlotterer, Oliver

doi:10.1103/physrevlett.118.161601

Cited by 79 publications

(106 citation statements)

References 74 publications

(135 reference statements)

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“…21 See Section 5.3 of [98] for a recent account on the key challenges in setting up loop-level KLT relations among string amplitudes from the viewpoint of intersection theory [99]. A field-theory version of one-loop KLT relations among loop integrands in gauge theories and supergravity has been derived from ambitwistor strings [100,101]. A connection with the present results may be investigated by adapting the generating functions of this work to the chiral-splitting formalism [102][103][104], where a string-theory analogue of the loop momentum is introduced at the expense of obscuring modular invariance.…”

Section: Discussionmentioning

confidence: 99%

All-order differential equations for one-loop closed-string integrals and modular graph forms

Gerken

Kleinschmidt

Schlotterer

2020

J. High Energ. Phys.

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140

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We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the first-order Cauchy-Riemann and secondorder Laplace equations for the generating functions for any number of external states. The low-energy expansion of such torus integrals introduces infinite families of non-holomorphic modular forms known as modular graph forms. Our results generate homogeneous first-and second-order differential equations for arbitrary such modular graph forms and can be viewed as a step towards all-order low-energy expansions of closed-string integrals. arXiv:1911.03476v2 [hep-th] 21 Jan 2020 F Derivation of component equations at three points 65 F.1 General Cauchy-Riemann component equations at three points 66 F.2 Examples of Cauchy-Riemann component equations at three points 67 F.3 Further examples for Laplace equations at three points 68 -ii -10The subscript of ∇DG aims to avoid confusion with the differential operators of Sections 3.1 and 3.2 and refers to the authors D'Hoker and Green of [9] which initiated the systematic study of relations between modular graph forms via repeated action of (2.59).

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Section: Discussionmentioning

confidence: 99%

All-order differential equations for one-loop closed-string integrals and modular graph forms

Gerken

Kleinschmidt

Schlotterer

2020

J. High Energ. Phys.

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140

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“…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.…”

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confidence: 99%

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

Geyer

Monteiro

Stark-Muchão

2019

J. High Energ. Phys.

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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...

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“…Here κ is the gravitational coupling, S i are symmetry factors, 1=d α i are (possibly massive) propagators, and D is the spacetime dimension. For gauge-theory amplitudes that lack manifest color-kinematics duality, generalized double copy constructions have been proposed [29]. The freedom of choosing the two gauge theories is critical for having a double copy description for large families of (super)gravities.…”

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Gauged Supergravities and Spontaneous Supersymmetry Breaking from the Double Copy Construction

et al. 2018

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Supergravities with gauged R symmetry and Minkowski vacua allow for spontaneous supersymmetry breaking and, as such, provide a framework for building supergravity models of phenomenological relevance. In this Letter, we initiate the study of double copy constructions for these supergravities. We argue that, on general grounds, we expect their scattering amplitudes to be described by a double copy of the type (spontaneously broken gauge theory)⊗ (gauge theory with broken supersymmetry). We present a simple realization in which the resulting supergravity has Uð1Þ R gauge symmetry, spontaneously broken N ¼ 2 supersymmetry, and massive gravitini. This is the first instance of a double copy construction of a gauged supergravity and of a theory with spontaneously broken supersymmetry. The construction extends in a straightforward manner to a large family of gauged Yang-Mills-Einstein supergravity theories with or without spontaneous gauge-symmetry breaking.

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New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

Cited by 79 publications

References 74 publications

All-order differential equations for one-loop closed-string integrals and modular graph forms

All-order differential equations for one-loop closed-string integrals and modular graph forms

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

Gauged Supergravities and Spontaneous Supersymmetry Breaking from the Double Copy Construction

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