Four-dimensional ambitwistor strings and form factors of local and Wilson line operators

We show that 10D spinor helicity formalism can be understood as spinor moving frame approach to supersymmetric particles extended to the description of amplitudes. This allows us to develop the spinor helicity formalism for 11D supergravity and a new constrained superfield formalism for 10D SYM and 11D SUGRA amplitudes. We show how the constrained on-shell superfields, one-particle counterparts of the superamplitudes, can be obtained by quantization of massless superparticle mechanics. We make some stages towards the calculation of amplitudes of 10D SYM and 11D SUGRA in this framework. In particular we have found supersymmetric Ward identities for constrained amplitudes and an especially convenient gauge, fixed on the spinor frame variables corresponding to scattered particles, which promises to be an extremely useful tool for further development of our approach. We also discuss a candidate for generalization of the BCFW recurrent relations for the constrained tree superamplitudes, indicate and discuss a problem of dependence of the expressions obtained with it on a deformation vector, which is not fixed uniquely in higher dimensional D > 4 cases.variables; this fact does not diminish the significance of these which were used quite extensively in [18].2 Also a momentum twistor formalism, alternative (dual) to the standard twistor approach and related to dual superconformal symmetry [9], rather than to the standard conformal symmetry of N = 4 SYM, was developed in [22,23]. 3 The identification of spinor helicity variables with Lorentz harmonics were noticed in [33] and used there to construct D=5 spinor helicity formalism. 4 The spinor moving frame approach for D=4 and D=10 superstrings was proposed in [38] and elaborated in [39], for 11D supermembrane in [40] and for the generic super-p-branes from the 'standard brane scan ' -in [41]. The synthesis of spinor moving frame approach with the so-called STV (Sorokin-Tkach-Volkov) approach to superparticles and superstrings [42,43,44] (see [45] for the review and more references) resulted in the development of the superembedding approach to superstrings and super-p-branes [46]. In particular, in the frame of this approach (also reviewed in [45]) the equations of motion of the M-theory 5-brane had been obtained in [47] some months before the covariant actions was constructed in [48] and [49].

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confidence: 99%

Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity

Bandos

2018

“…This situation is quite different from that of on-shell scattering amplitudes, for which the two formulas can be smoothly deformed into one another, and it may teach us important lessons about applying the Graßmannian formalism and the connected prescription to form factors or more general off-shell and/or non-planar objects. As a way forward it may be fruitful to note the role such smooth deformations play in showing the equivalence of similar integral formulas in the case of form factors of Wilson line operators [16].…”

Section: Discussionmentioning

confidence: 99%

“…In analogy with the amplitude connected prescription [24], in [29] and [30] a similar formula was obtained for form factors of the chiral part of the stress tensor operator. This representation was given an ambitwistor string interpretation in [29] and [16]. Here we review the derivation of [29] for the form factor connected formula in the link representation.…”

Section: Brief Review Of the Connected Prescription And Link Represenmentioning

confidence: 99%

“…The operator with the most well-studied form factors [11,12,13,14,15,16] is the chiral part of the stress-tensor multiplet T (x, θ + ), which is a protected supersymmetric operator. It can be expanded in harmonic superspace 2 Graßmann coordinates θ +a α , with α, a = 1, 2, and contains the operator Tr(φ 2 ), with φ one of the scalars of the theory, as the top component and the on-shell Lagrangian of N= 4 SYM as the coefficient of the highest power in θ + .…”

Section: Introductionmentioning

confidence: 99%

“…Aspects of this deformation play an important role in the derivation of similar integrals for form factors of Wilson line operators from the ambitwistor string in[16]. It would be very interesting to see if the approach of this work can shed more light on this issue.…”

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confidence: 97%

See 2 more Smart Citations

A note on NMHV form factors from the Graßmannian and the twistor string

Meidinger

Nandan

Penante

et al. 2017

In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in N = 4 superconformal Yang-Mills theory. We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes.

Full-color three-loop three-point form factors in 𝒩 = 4 SYM

Lin

Yang

Zhang

2022

We present the detailed computation of full-color three-loop three-point form factors of both the stress-tensor supermultiplet and a length-three BPS operator in 𝒩 = 4 SYM. The integrands are constructed based on the color-kinematics (CK) duality and generalized unitarity method. An interesting observation is that the CK-dual integrands contain a large number of free parameters. We discuss the origin of these free parameters in detail and check that they cancel in the simplified integrands. We further perform the numerical evaluation of the integrals at a special kinematics point using public packages FIESTA and pySecDec based on the sector-decomposition approach. We find that the numerical computation can be significantly simplified by expressing the integrals in terms of uniformly transcendental basis, although the final three-loop computations still require large computational resources. Having the full-color numerical results, we verify that the non-planar infrared divergences reproduce the non-dipole structures, which firstly appear at three loops. As for the finite remainder functions, we check that the numerical planar remainder for the stress-tensor supermultiplet is consistent with the known result of the bootstrap computation. We also obtain for the first time the numerical results of the three-loop non-planar remainder for the stress-tensor supermultiplet as well as the three-loop remainder for the length-three operator.