From maximal to minimal supersymmetry in string loop amplitudes

Berg, Mark A.; Buchberger, Igor; Schlotterer, Oliver

doi:10.1007/jhep04(2017)163

Cited by 31 publications

(87 citation statements)

References 176 publications

(524 reference statements)

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“…These partial integrands inherit BCJ relations (5), (6) from tree level, and similar relations for partial integrands of one-loop EYM amplitudes (25). Most importantly, they are suitable for constructing one-loop gravity integrands through our main result (7), a one-loop generalization of the KLT formula [1] valid for the gravitational double copies of a wide range of gauge theories.…”

Section: Conclusion and Further Directionsmentioning

confidence: 81%

“…The infrared regularization prescription of [25] for SYM amplitudes in D ≤ 6 with 8 supercharges gives rise to three-point partial integrands…”

Section: B 3pt Half-maximalmentioning

confidence: 99%

“…Note that the naively 24-dimensional BCJ basis of partial integrands is again degenerate by maximal supersymmetrythe gauge invariant organization of [26] leaves three linearly independent kinematic factors, two permutations of A tree YM (1, 2, 3, 4, 5) and one ℓ-dependent invariant. D. 4pt half-maximal: In the four-point SYM integrands of [25], all the non-trivial tree-level diagrams involving leg 1 are absorbed into the gauge invariant quantities C 1|ijk , C …”

Section: B 3pt Half-maximalmentioning

confidence: 99%

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

Schlotterer

2017

Phys. Rev. Lett.

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In this letter, we extend the tree-level Kawai-Lewellen-Tye (KLT) and Bern-Carrasco-Johansson (BCJ) amplitude relations to loop integrands of gauge theory and gravity. By rearranging the propagators of gauge and gravity loop integrands, we propose the first manifestly gauge-and diffeomorphism invariant formulation of their double-copy relations. The one-loop KLT formula expresses gravity integrands in terms of more basic gauge invariant building blocks for gauge-theory amplitudes, dubbed partial integrands. The latter obey a one-loop analogue of the BCJ relations, and both KLT and BCJ relations are universal to bosons and fermions in any number of spacetime dimensions and independent on the amount of supersymmetry. Also, one-loop integrands of Einstein-Yang-Mills (EYM) theory are related to partial integrands of pure gauge theories.

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Section: Conclusion and Further Directionsmentioning

confidence: 81%

“…The infrared regularization prescription of [25] for SYM amplitudes in D ≤ 6 with 8 supercharges gives rise to three-point partial integrands…”

Section: B 3pt Half-maximalmentioning

confidence: 99%

Section: B 3pt Half-maximalmentioning

confidence: 99%

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

Schlotterer

2017

Phys. Rev. Lett.

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“…, b n−2 , 0, b n ), respectively, then the only places where the points z n−1 and z n 6 Also see e.g. [65][66][67] for earlier work on RNS spin sums, [68][69][70][71][72] for g in one-loop amplitudes in the pure-spinor formalism and [73,74] for applications to RNS one-loop amplitudes with reduced supersymmetry. 7 String-theory integrals can also involve integrals over ∂z i f…”

Section: Relations Between Component Integralsmentioning

confidence: 99%

“…However, additional contributions with (non-negative) weights (|A| − k, |B| − k), k ∈ N arise from interactions between left and right-movers: Both the direct contractions between left-and right-moving world-sheet bosons and the contribution of (2.7) to integrations by parts convert one unit of holomorphic and non-holomorphic modular weight into a factor of (Im τ ) −1 , see e.g. [3,74,79].…”

Section: B5 Verifying Two-point Cauchy-riemann Equationsmentioning

confidence: 99%

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

2020

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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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Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes

Garozzo

Queimada

Schlotterer

2019

J. High Energ. Phys.

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We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators α F 3 and α 2 F 4 . Based on Berends-Giele recursions, the tensor structure of these amplitudes is compactly organized via off-shell currents. On the one hand, we present manifestly cyclic representations, where the complexity of the currents is systematically reduced. On the other hand, the duality between color and kinematics due to Bern, Carrasco and Johansson is manifested by means of non-linear gauge transformations of the currents. We exploit the resulting notion of Bern-Carrasco-Johansson gauge to provide explicit and manifestly local double-copy representations for gravitational amplitudes involving α R 2 and α 2 R 3 operators. arXiv:1809.08103v1 [hep-th] 21 Sep 2018 45 A.3 Gauge algebra 47 B The explicit form of gauge scalars towards BCJ gauge 50 B.1 The local building block h 12345 50 B.2 An alternative expression for H 1234 51 B.3 The Berends-Giele version H 12345 52 C Deriving a BCJ representation for (YM+F 3 +F 4 ) amplitudes 52 -1 -1 The low-energy effective action of the open bosonic string involves another operator ∼ ζ2α 2 F 4 at the mass dimensions in (1.1) which will not be discussed in this article. Said ζ2α 2 F 4 -operator is also known from the superstring and cannot be reconciled with the BCJ duality [18]. 2 See [ 23,24] for earlier work on the interplay of the KLT relations at the three-and four-point level with gravitational matrix elements of R 2 , R 3 operators and F 3 , F 4 -deformed gauge-theory amplitudes.3 In slight abuse of terminology, we will usually refer to the matrix elements from higher-mass-dimension operators as "amplitudes". In the case at hand, we will be interested in contributions from single-or doubleinsertions of α R 2 operators and single-insertions of α 2 R 3 4 See [27,28] for generating series of Berends-Giele currents, their non-linear gauge transformations and BCJ gauge in ten-dimensional SYM.5 Said higher-derivative extension of the NLSM is defined by the ζ2α 2 -order of abelian Z-theory [44].

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From maximal to minimal supersymmetry in string loop amplitudes

Cited by 31 publications

References 176 publications

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

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

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

Berends-Giele currents in Bern-Carrasco-Johansson gauge for F3- and F4-deformed Yang-Mills amplitudes

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