Scattering amplitudes — Wilson loops duality for the first non-planar correction

We compute the three-loop scattering amplitude of four gravitons in N = 8 supergravity. Our results are analytic formulae for a Laurent expansion of the amplitude in the regulator of dimensional regularisation. The coefficients of this series are closed formulae in terms of well-established harmonic poly-logarithms. Our results display a remarkable degree of simplicity and represent an important stepping stone in the exploration of the structure of scattering amplitudes. In particular, we observe that to this loop order the four graviton amplitude is given by uniform weight 2L functions, where L is the loop order.

Section: Introductionmentioning

confidence: 99%

Four-graviton scattering to three loops in $$ \mathcal{N}=8 $$ supergravity

Henn

Mistlberger

2019

“…The existence of such a subgroup of dual conformal symmetry, called directional dual conformal symmetry, has been recently unveiled and used in the computation of certain non-planar loop integrals [32][33][34] (see also Ref. [35]). The projection by p 1 in fact removes all the terms which would break the dual conformal covariance, as can be clearly seen by taking b ∝ p 1 in Eq.…”

Section: Hints For Dual Conformal Symmetrymentioning

confidence: 99%

Conformal invariance of the one-loop all-plus helicity scattering amplitudes

Henn

Power

Zoia

2020

The massless QCD Lagrangian is conformally invariant and, as a consequence, so are the tree-level scattering amplitudes. However, the implications of this powerful symmetry at loop level are only beginning to be explored systematically. Even for finite loop amplitudes, the way conformal symmetry manifests itself may be subtle, e.g. in the form of anomalous conformal Ward identities. As they are finite and rational, the oneloop all-plus and single-minus amplitudes are a natural first step towards understanding the conformal properties of Yang-Mills theory at loop level. Remarkably, we find that the one-loop all-plus amplitudes are conformally invariant, whereas the single-minus are not. Moreover, we present a formula for the one-loop all-plus amplitudes where the symmetry is manifest term by term. Surprisingly, each term transforms covariantly under directional dual conformal variations. We prove the formula directly using recursive techniques, and check that it has the correct physical factorisations.

“…which is the statement that the structure constants are free from wrappings for l C L = O(1). 22 According to [55][56][57] the pp-wave SFT vertex relates to amputated structure constants. We read it…”

Section: Wrapping and Stringmentioning

confidence: 99%

“…On the other hand, in a different vein, the integrability technology, see [13] for a review, fostered the development of form-factor methods aiming at solving correlation functions, or scattering amplitudes, for any g in the large N c limit [14][15][16][17][18][19][20][21][22]. Among these techniques, the hexagon method appears as the most versatile.…”

Section: Introductionmentioning

confidence: 99%

Three-point functions at strong coupling in the BMN limit

Basso

Zhong

2020

We consider structure constants of single-trace operators at strong coupling in planar N = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavylight correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.