Double copy structure of CFT correlators

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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“…Similar results were observed for other representations for AdS amplitudes and CFT correlators, see e.g. [102].…”

Section: Discussionsupporting

confidence: 87%

Spinor-Helicity Formalism for Massless Fields in AdS4

Nagaraj

Ponomarev

2019

Phys. Rev. Lett.

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“…For instance, KLT-like relations have been carried out in the context of cosmology [74]. Similarly, double copy like relations have been explored and are successfully realized for three point CFT correlators [75]. It is an interesting question whether these analyses can be further developed for holographic settings, and we hope that our work can assist in this direction.…”

Section: Resultsmentioning

confidence: 94%

Towards the higher point holographic momentum space amplitudes. Part II. Gravitons

Albayrak

Kharel

2019

J. High Energ. Phys.

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In this follow up paper, we calculate higher point tree level graviton Witten diagrams in AdS 4 via bulk perturbation theory. We show that by rearranging the bulk to bulk graviton propagators, the calculations effectively reduce to the computation of a scalar factor. Analogous to the amplitudes for vector boson interactions we computed in the previous paper, scalar factors for the graviton exchange diagrams also become relatively simple when written in momentum space. We explicitly calculate higher point correlators and discuss how this momentum space formalism makes flat space and collinear limits simpler.

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“…Apart from flat-space scattering amplitudes, the double-copy structure has been found in other gravitational settings, such as for non-trivial curved backgrounds [39,40]. Remarkably, a number of important classical solutions to Einstein's field equations -including the Schwarzschild and Kerr black holes -may be expressed in terms of solutions in the underlying gauge theory [41][42][43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Double copy for massive quantum particles with spin

Johansson

Ochirov

2019

J. High Energ. Phys.

157

182

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The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. In this paper we elaborate on the double copy that yields amplitudes in gravitational theories coupled to flavored massive matter with spin, which is relevant to the problems of black-hole scattering and gravitational waves. Our construction benefits from making the little group explicit for the massive particles, as shown on lower-point examples. For concreteness, we focus on the double copy of QCD with massive quarks, for which we work out the gravitational Lagrangian up to quartic scalar and vector-scalar couplings. We find new gauge-invariant double-copy formulae for tree-level amplitudes with two distinct-flavor pairs of matter and any number of gravitons. These are similar to, but inherently different from, the well-known Kawai-Lewellen-Tye formulae, since the latter only hold for the double copy of purely adjoint gauge theories.

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Double copy structure of CFT correlators

Cited by 124 publications

References 128 publications

Spinor-Helicity Formalism for Massless Fields in AdS4

Spinor-Helicity Formalism for Massless Fields in AdS4

Towards the higher point holographic momentum space amplitudes. Part II. Gravitons

Double copy for massive quantum particles with spin

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