Single-Valued Integration and Superstring Amplitudes in Genus Zero

Brown, Francis; Dupont, Clément

doi:10.1007/s00220-021-03969-4

Cited by 50 publications

(94 citation statements)

References 37 publications

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“…It turns out that for a suitable parametrization of M 0,n , these amplitudes can be written as an integral I A n−3 in the form (1.3), where the p j (x) are the F -polynomials for the type A n−3 cluster algebra. The importance of the u ij -variables appears in the rewriting (see [3,Section 9] or [10,Section 3])…”

Section: 3mentioning

confidence: 99%

Cluster Configuration Spaces of Finite Type

Arkani-Hamed¹,

He²,

Lam³

2021

SIGMA

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For each Dynkin diagram D, we define a "cluster configuration space" M D and a partial compactification M D . For D = A n−3 , we have M An−3 = M 0,n , the configuration space of n points on P 1 , and the partial compactification M An−3 was studied in this case by Brown. The space M D is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular functions on M D are generated by coordinates u γ , in bijection with the cluster variables of type D, and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes.

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Section: 3mentioning

confidence: 99%

Cluster Configuration Spaces of Finite Type

Arkani-Hamed¹,

He²,

Lam³

2021

SIGMA

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“…The generalized KLT kernel is again the inverse of an intersection matrix with trigonometric functions in its entries which we derive from adjacency properties of Stasheff polytopes [55]. Our results furnish an explicit realization of several of the general mathematical concepts relating double copy, single-valued integration and string amplitudes [51,56]. Many all-multiplicity statements in this work are left as conjectures, and we hope that the ideas of the references set the stage to find rigorous proofs.…”

Section: Jhep05(2021)053mentioning

confidence: 81%

“…• At the level of the MZVs in their α -expansion, closed-string integrals C (n,n−3)ωaωb are single-valued images [3,46] of disk integrals [7,[47][48][49][50][51] γa ω b of open strings with suitably chosen integration contours γ a .…”

Section: Jhep05(2021)053mentioning

confidence: 99%

“…(n,n−3) ab ifω (n,p) a are replaced by suitably chosen Parke-Taylor forms [7,[47][48][49][50][51]56]:…”

Section: General Formulaementioning

confidence: 99%

“…However, this is not a fully rigorous proof since the use of the single-valued map relies on transcendentality conjectures on MZVs. The techniques of Brown and Dupont [51,56] in turn should allow for a proof without any such assumptions.…”

Section: Jhep05(2021)053mentioning

confidence: 99%

See 2 more Smart Citations

Coaction and double-copy properties of configuration-space integrals at genus zero

Britto

Mizera

Rodriguez

et al. 2021

J. High Energ. Phys.

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We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension α′ or the dimensional-regularization parameter ϵ of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in ($$ \mathfrak{p} $$ p , 2) minimal models, which can be normalized to become uniformly transcendental in the $$ \mathfrak{p} $$ p → ∞ limit.

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Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings

Gerken

Kleinschmidt

Schlotterer

2019

J. High Energ. Phys.

100

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We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude, the integrals over torus punctures are systematically evaluated in terms of modular graph forms, certain nonholomorphic modular forms. For a specific torus integral, the modular graph forms in the low-energy expansion are related to the elliptic multiple zeta values from the analogous openstring integrations over cylinder boundaries. The detailed correspondence between these modular graph forms and elliptic multiple zeta values supports a recent proposal for an elliptic generalization of the single-valued map at genus zero. (2,0) 12|34 66 D.2.2 Rewriting the integral I (4,0) 12|34 66 D.2.3 Towards a uniform-transcendentality basis 67 -ii -D.3 Efficiency of the new representations for higher-order expansions 67 E The elliptic single-valued map at the third order in α 68 E.1 Modular transformation of iterated Eisenstein integrals 68 E.2 The third α -order of I (2,0) 1234 and iterated Eisenstein integrals 69

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Single-Valued Integration and Superstring Amplitudes in Genus Zero

Cited by 50 publications

References 37 publications

Cluster Configuration Spaces of Finite Type

Cluster Configuration Spaces of Finite Type

Coaction and double-copy properties of configuration-space integrals at genus zero

Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings

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