A Riccati type PDE for light-front higher helicity vertices

Bengtsson, Anders K.H.

doi:10.1007/jhep09(2014)105

Cited by 21 publications

(21 citation statements)

References 90 publications

(198 reference statements)

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“…Additional motivation to address this question is related to higher-spin theories. It was discovered recently [11,34] that the spinor-helicity formalism allows to construct additional consistent cubic amplitudes compared to those available within the framework that employs Lorentz tensors. This observation is based on the comparison of two classifications available in both approaches.…”

Section: Jhep06(2020)068 Introductionmentioning

confidence: 99%

Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials

Nagaraj

Ponomarev

2020

J. High Energ. Phys.

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Section: Jhep06(2020)068 Introductionmentioning

confidence: 99%

Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials

Nagaraj

Ponomarev

2020

J. High Energ. Phys.

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“…This begs the question: is there any natural generalization of the spinor-helicity formalism to AdS, which allows to deal with amplitudes of massless fields as efficiently as in flat space?Additional motivation to address this question is related to higher-spin theories. It was discovered recently [11,34] that the spinor-helicity formalism allows to construct additional consistent cubic amplitudes compared to those available within the framework that employs Lorentz tensors. This observation is based on the comparison of two classifications available 1 These results were obtained employing the light-cone deformation procedure, which is closely connected to the spinor-helicity formalism [37][38][39].2 An independent bulk formulation of higher-spin theories was proposed in [46,47].…”

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confidence: 99%

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confidence: 99%

Spinor-Helicity Formalism for Massless Fields in AdS4

Nagaraj

Ponomarev

2019

Phys. Rev. Lett.

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In a recent letter we suggested a natural generalization of the flat-space spinorhelicity formalism in four dimensions to anti-de Sitter space. In the present paper we give some technical details that were left implicit previously. For lower-spin fields we also derive potentials associated with the previously found plane wave solutions for field strengths. We then employ these potentials to evaluate some three-point amplitudes. This analysis illustrates a typical computation of an amplitude without internal lines in our formalism.In recent years significant progress was achieved in amplitudes' computations as well as in understanding of various hidden structures underlying them. This is especially true for theories of massless particles in four dimensions. For these theories one can choose convenient kinematic variables that lead to what is known as the spinor-helicity formalism. This formalism allows to compute amplitudes efficiently and produces them in an extremely compact form. This is typically illustrated by the Parke-Taylor formula [1], which gives a single-term expression for a tree-level MHV n-point amplitude in the Yang-Mills theory. The spinor-helicity formalism also fits together nicely with other techniques used for amplitudes' computations. For review on modern amplitude methods and on the spinor-helicity formalism, see [2][3][4]. The success of the spinor-helicity formalism for theories of massless particles in four dimensions motivated its various extensions -to other dimensions [5][6][7][8][9] and to massive fields [10][11][12][13].Another line of research that lead to important developments in recent years is the AdS/CFT correspondence. It is a conjectured duality between gravitational theories in AdS space and conformal theories on its boundary [14][15][16]. The AdS/CFT correspondence provides us with new tools to address important problems of quantum gravity and strongly coupled systems. On the AdS side perturbative observables are computed by Witten diagrams, which can be regarded as the AdS counterpart of flat scattering amplitudes. These diagrams can be expressed in different representations: in terms of boundary coordinates that label external lines, in terms of the associated Fourier or Mellin space variables or presented in the form of the conformal block decomposition, see [17][18][19][20][21][22][23][24][25][26][27][28] for a far from complete list of references. Each of these representations has its own virtues and for each of them major progress was achieved in recent years. In particular, more efficient methods of computing Witten diagrams were developed, relations between the analytic structure of amplitudes and types of bulk processes were understood, it was found how take the flatspace limit of Witten diagrams, thus, reproducing the associated flat scattering amplitudes. Moreover, these results can be extended to dS space producing de Sitter space correlators, which, in turn, are closely related to inflationary correlators, see e.g. [29][30][31][32][33]. Despite these successes, ...

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“…There emerges a series of works combining these two approaches to study the spinor helicity amplitudes [19,22,23], the most notable discovery being a mismatch between the light-cone and covariant approaches: there are cubic vertices existing in light-cone approach but are absent in the covariant approach [19,[21][22][23]. As it turns out, the missing part is crucial for the existence of the higher-spin theory in 4d Minkowski spacetime, as pointed out by [19] and [23].…”

Section: Jhep12(2017)048mentioning

confidence: 99%

“…Thus, we reproduce the mismatch between the covariant approach and the light-cone approach. For further discussions on this mismatch, the readers are referred [19,[21][22][23].…”

Section: Helicity Amplitudesmentioning

confidence: 99%

On-shell gauge invariant three-point amplitudes

Sun

Cheung

2017

J. High Energ. Phys.

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Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches.Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field φ and an antisymmetric rank-2 tensor field A µν . Despite the well-known fact that in 4 dimensions rank-2 antisymmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.

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A Riccati type PDE for light-front higher helicity vertices

Cited by 21 publications

References 90 publications

Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials

Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials

Spinor-Helicity Formalism for Massless Fields in AdS4

On-shell gauge invariant three-point amplitudes

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