Propagators, BCFW recursion and new scattering equations at one loop

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: Linearized Versus Quadratic Propagatorsmentioning

confidence: 99%

Section: Jhep12(2021)007mentioning

confidence: 99%

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

Edison

Guillen

Johansson

et al. 2021

“…Over the past few years a related approach based on ambitwistor string theory has emerged, see, e.g., [21][22][23][24][25][26][27] (various other recent worldsheet approaches to color-kinematics duality include [28][29][30][31][32][33][34][35][36][37]), which gives a handle on the problem of constructing BCJ numerators, at a cost of introducing linearized propagators which need to be transformed into quadratic ones using non-trivial partial fraction identities. Despite many successes of this research direction, our goal here is to obtain Feynman diagrams directly from worldsheet degenerations, which at present is understood most appropriately in the case of string theory.…”

Section: Jhep03(2021)048mentioning

confidence: 99%

Loop amplitudes monodromy relations and color-kinematics duality

Casali

Mizera

Tourkine

2021

Color-kinematics duality is a remarkable conjectured property of gauge theory which, together with double copy, is at the heart of a wealth of new developments in scattering amplitudes. So far, its validity has been verified in most cases only empirically, with limited ab initio understanding beyond tree-level. In this paper we provide initial steps in a first-principle understanding of color-kinematics duality and double-copy at loop level, through a detailed analysis of the field-theory limit of the monodromy relations of string theory at one loop. In this limit, we dissect the type of Feynman graphs generated and the relations they obey. We find that graphs with contact-terms are unavoidable and are generated in the field theory limit of “bulk” contours which do not have a standard physical interpretation in string perturbation theory. We show how they are related to ambiguities in the definition of the loop momentum and that their role is precisely to cancel those ambiguities.

“…This recursion was generalised to all-loop integrands in planar N = 4 SYM in [7]. See [29] for recent progress on loop-level recursion in generic theories.…”

Section: Jhep01(2021)181mentioning

confidence: 99%

$$ \mathcal{N} $$ = 7 On-shell diagrams and supergravity amplitudes in momentum twistor space

Armstrong

Farrow

Lipstein

2021

Self Cite

We derive an on-shell diagram recursion for tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 7 supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in momentum twistor space to non-MHV amplitudes. In particular, we recast five and six-point NMHV amplitudes in terms of $$ \mathcal{N} $$ N = 7 R-invariants analogous to those of $$ \mathcal{N} $$ N = 4 super-Yang-Mills, which makes cancellation of spurious poles more transparent. Above 5-points, this requires defining momentum twistors with respect to different orderings of the external momenta.