Loop amplitudes monodromy relations and color-kinematics duality

In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D2kFn and D2kRn in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension α′. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in α′. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

Section: Discussionmentioning

confidence: 99%

Section: Relations Among One-loop Matrix Elementsmentioning

confidence: 99%

See 1 more Smart Citation

One-loop matrix elements of effective superstring interactions: α′-expanding loop integrands

Edison

Guillen

Johansson

et al. 2021

“…But we know that these limits constitute a local property of the Riemann surface and therefore must be independent of its genus. These results together with the analysis of [30] lead to the following expectation: The field-theory limit of the one-loop string correlators integrated along different vertex insertion orderings should give rise to a local representation for SYM one-loop integrands that satisfy the BCJ color-kinematics duality. As an illustration of this method -to be fully developed in the next sections -let us apply it in the simplest case of the five-point SYM integrand/amplitude following from the string correlator (1.2).…”

Section: Jhep07(2021)031mentioning

confidence: 90%

Local BCJ numerators for ten-dimensional SYM at one loop

Bridges

Mafra

2021

We obtain local numerators satisfying the BCJ color-kinematics duality at one loop for super-Yang-Mills theory in ten dimensions. This is done explicitly for six points via the field-theory limit of the genus-one open superstring correlators for different color orderings, in an analogous manner to an earlier derivation of local BCJ-satisfying numerators at tree level from disk correlators. These results solve an outstanding puzzle from a previous analysis where the six-point numerators did not satisfy the color-kinematics duality.

“…The discussion in this work calls for a generalization from the Riemann sphere to higher-genus surfaces and elliptic flavors of MZVs and multiple polylogarithms. Following the string-theory nomenclature, the associated twisted homologies are governed by the loop-level monodromy relations [130][131][132][133] between integration cycles some but not all of which are realized in open-string scattering. On the cohomology side, candidate bases for integration-by-parts inequivalent forms of open-string integrals were proposed in [25,26] and [134,135] for one and two unintegrated punctures, respectively.…”

Section: Jhep05(2021)053mentioning

confidence: 99%

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

Britto

Mizera

Rodriguez

et al. 2021

Self Cite

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.