On-shell diagrams for N $$ \mathcal{N} $$ = 8 supergravity amplitudes

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].

Section: From the Candidate Bcfw Relation To An Expression For 10d Symentioning

confidence: 99%

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

Bandos

2018

“…Even though they have been most prominently featured in the realm of supersymmetric theories [21,[129][130][131][132][133] (see e.g. [134,135] for some exceptions), they can generally be defined from first principles without reference to (off-shell) loop integrands in any quantum field theory.…”

Section: Jhep06(2017)059mentioning

confidence: 99%

Prescriptive unitarity

Bourjaily

Herrmann

Trnka

2017

116

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N k MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those without planarity, supersymmetry, or massless spectra defined in any number of dimensions.

“…Similarly, the form of 3-point N = 8 4D supergravity superamplitude, which is essentially the square of the N = 4 4D SYM one (see e.g. [11,12]), suggests the following gauge fixed expression for the basic 3-point superamplitude of 11D supergravity,…”

Section: Analytical 3-point Superamplitude Of D = 11 Supergravitymentioning

confidence: 99%

“…An impressive recent progress in calculation of multi-loop amplitudes of d=4 supersymmetric Yang-Mills (SYM) and supergravity (SUGRA) theories, especially of their maximally supersymmetric versions N = 4 SYM and N = 8 SUGRA [1,2,3,4,5], was reached in its significant part with the use of spinor helicity formalism and of its superfield generalization [6,7,9,10,11,12,13]. This latter works with superamplitudes depending on additional fermionic variables and unifying a number of different amplitudes of the bosonic and fermionic fields from the SYM or SUGRA supermultiplet.…”

Section: Introductionmentioning

confidence: 99%

An analytic superfield formalism for tree superamplitudes in D=10 and D=11

Bandos

2018

Tree amplitudes of 10D supersymmetric Yang-Mills theory (SYM) and 11D supergravity (SUGRA) are collected in multi-particle counterparts of analytic on-shell superfields. These have essentially the same form as their chiral 4D counterparts describing N = 4 SYM and N = 8 SUGRA, but with components dependent on a different set of bosonic variables. These are the D=10 and D=11 spinor helicity variables, the set of which includes the spinor frame variable (Lorentz harmonics) and a scalar density, and generalized homogeneous coordinates of the coset SO(D−2) SO(D−4)⊗U (1) (internal harmonics). We present an especially convenient parametrization of the spinor harmonics (Lorentz covariant gauge fixed with the use of an auxiliary gauge symmetry) and use this to find (a gauge fixed version of) the 3-point tree superamplitudes of 10D SYM and 11D SUGRA which generalize the 4 dimensional anti-MHV superamplitudes.