Double-Copy Structure of One-Loop Open-String Amplitudes

Mafra, Carlos R.; Schlotterer, Oliver

doi:10.1103/physrevlett.121.011601

Cited by 48 publications

(93 citation statements)

References 44 publications

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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%

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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Section: Relations Between Component Integralsmentioning

confidence: 99%

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

2020

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“…It would be particularly interesting to study the relations to the recently-found doublecopy structures at genus-one [48,65,66] in this context. The transformation properties in (A.3) can be used to show that there is an extra phase that the prime form picks up when z and w are the position of particles on different boundaries, compared to when they are on the same boundary.…”

Section: Towards Klt Relationsmentioning

confidence: 99%

Monodromy relations from twisted homology

Casali

Mizera

Tourkine

2019

J. High Energ. Phys.

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We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations involving loop integrands of open-string theories for any number of external particles and, for the first time, to arbitrary genus. In the non-planar sector, these relations contain seemingly unphysical contributions, which we argue clarify mismatches in previous literature. The text is mostly self-contained and presents a concise introduction to twisted homologies. As a result of this powerful formulation, we can propose estimates on the number of independent loop integrands based on Euler characteristics of the relevant configuration spaces, leading to a higher-genus generalization of the famous (n − 3)! result at genus zero.We then formulate twisted homology on such a cut Riemann surface keeping loop momenta µ I as well as surface moduli Ω IJ fixed. Therefore all statements we make are about loop integrands for open strings. The introduction of loop momenta also helps in the interpretation of our results in the field-theory limit.Key identities used to deduce relations between different color-ordered amplitudes at genus zero are the monodromy relations introduced by Plahte [1] and later studied in [2,4]. From the perspective of twisted homology, they become simply a statement of the vanishing of terms which are a total boundary under the twisted boundary operator [16,24], that is, contours that can be deformed to a point. Using this framework one can prove that the dimension of twisted homology of M 0,n is (n−3)! [25] (in the physics literature this result first appeared in [2,4]), which has a geometric interpretation in terms of the Euler characteristic of M 0,n .Our setup essentially trivializes finding monodromy relations for higher-genus surfaces.-3 -This allows us to write down explicit identities for all planar open-string integrands with particle inserted on any boundary to arbitrary genus g, 1 arbitrary number of punctures n, all orders in α , and any external string state. For the correct counting of the number of independent cycles it is important to realize that there are always two monodromy relations for each surface, obtained from contracting the contours C + and C − in Figure 1. These two relations explain heuristically the reduction from the naive (n − 1)! to (n − 3)! distinct tree-level amplitudes. If one builds up recursively the amplitude by adding punctures, at each step there are two fewer independent amplitudes resulting in the previous reduction. The story is sometimes presented differently in the literature, where complex conjugation, or real and imaginary parts, are invoked. While this is effectively identical to using these two relations we believe that the problem is better formulated in those terms. At low genus (g = 1, 2, 3), similar monodromy relations were recently written down in [30][31][32]46] and checked to the first couple of orders in α . These...

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“…[75]. More importantly, it would be highly desirable to apply our method to string correlators with massive states, as well as to cases at genus one [76][77][78][79][80][81][82]. On the other hand, the CHY half-integrands here contain explicit α ′ dependence, and it would be interesting to understand if there are worldsheet models, such as ambitwistor string [20,24,25] theory, underpin it (see [28] for some progress which gives at least correct three-point amplitudes).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

String correlators: recursive expansion, integration-by-parts and scattering equations

Teng

Zhang

2019

J. High Energ. Phys.

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We further elaborate on the general construction proposed in [1], which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for Yang-Mills-scalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combinations of Parke-Taylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding (DF ) 2 + YM + φ 3 amplitudes. It is the first closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles.

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Double-Copy Structure of One-Loop Open-String Amplitudes

Cited by 48 publications

References 44 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

Monodromy relations from twisted homology

String correlators: recursive expansion, integration-by-parts and scattering equations

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