AdS weight shifting operators

Costa, Miguel S.; Hansen, Tobias

doi:10.1007/jhep09(2018)040

Cited by 60 publications

(60 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, an operator that shifts the weight of the internal field was introduced in (4.58). Similar weight-shifting operators for conformal correlators in position space have recently been discovered in[68,98].…”

supporting

confidence: 63%

The cosmological bootstrap: inflationary correlators from symmetries and singularities

Arkani-Hamed

Baumann

Lee

et al. 2020

J. High Energ. Phys.

319

551

View full text Add to dashboard Cite

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a "spin-raising" operator relates it to the correlators associated with the exchange of particles with spin, while "weight-shifting" operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three-and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit. arXiv:1811.00024v3 [hep-th]

show abstract

supporting

confidence: 63%

The cosmological bootstrap: inflationary correlators from symmetries and singularities

Arkani-Hamed

Baumann

Lee

et al. 2020

J. High Energ. Phys.

319

551

View full text Add to dashboard Cite

show abstract

“…Refs. [32,65,66,33,67,68,69]. On the p-adic front, however, it is at present not well understood how to describe spinning degrees of freedom in a discrete bulk geometry.…”

Section: Discussionmentioning

confidence: 99%

p-adic Mellin amplitudes

Jepsen

Parikh

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

In this paper, we propose a p-adic analog of Mellin amplitudes for scalar operators, and present the computation of the general contact amplitude as well as arbitrary-point tree-level amplitudes for bulk diagrams involving up to three internal lines, and along the way obtain the p-adic version of the split representation formula. These amplitudes share noteworthy similarities with the usual (real) Mellin amplitudes for scalars, but are also significantly simpler, admitting closed-form expressions where none are available over the reals. The dramatic simplicity can be attributed to the absence of descendant fields in the p-adic formulation.

show abstract

“…[35,54,[79][80][81]. The same idea can also be used to generate more complicated Witten diagrams and conformal correlators from simpler ones [22,[82][83][84][85]. In the present section we will demonstrate how this approach can be implemented for three-point amplitudes in AdS 4 in the spinorhelicity representation.…”

Section: Helicity-changing Operatorsmentioning

confidence: 99%

Spinor-Helicity Formalism for Massless Fields in AdS4

Nagaraj

Ponomarev

2019

Phys. Rev. Lett.

View full text Add to dashboard Cite

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, ...

show abstract

AdS weight shifting operators

Cited by 60 publications

References 60 publications

The cosmological bootstrap: inflationary correlators from symmetries and singularities

The cosmological bootstrap: inflationary correlators from symmetries and singularities

p-adic Mellin amplitudes

Spinor-Helicity Formalism for Massless Fields in AdS4

Contact Info

Product

Resources

About