Spinning Witten diagrams

We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al.[1] to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk threepoint interaction vertices which give rise to all possible boundary three point structures. We highlight a direct connection between the representation of the conformal block as geodesic Witten diagram and the shadow operator formalism.

“…The authors use different techniques to address similar questions. Shorlty following the appearance of our work, two papers containing some overlap with our own appeared [61,62].…”

Section: Jhep11(2017)060mentioning

confidence: 95%

Spinning geodesic Witten diagrams

Dyer¹,

Freedman²,

Sully³

2017

“…Here, we directly evaluated the Fourier transform of the known result [99,100] for tree-level three-point Witten diagrams of scalar fields in Euclidean anti-de Sitter space (which is most naturally given by a Mellin-Barnes integral) and applying the dictionary spelled out in §2.5 to each propagator at the level of the Mellin integrand to obtain the corresponding late-time correlator in de Sitter space. This approach also straightforwardly extends to correlators of spinning fields, where it is readily applicable for totally symmetric fields in general d using the results derived in [43] for their tree-level three-point Witten diagrams. We shall demonstrate this in the following section for correlators involving a single totally symmetric spin-fields in general d, and discuss the more general spinning case in a forthcoming work [98].…”

Section: General External Scalarsmentioning

confidence: 99%

“…(4.87) + 2 −p 12 p 34 log(k 2 (p 12 + 1)(p 34 + 1)) − 2(γ − 1)p 12 p 34 + p 12 + p 34 kk 1 k 2 k 3 k 4 + O (1) . 43 To compare with (5.74) of [29] one needs to massage the above expression using some properties of the Dilogarithm function, including the identity:…”

Section: Simplifications and Subtleties Away From The Principal Seriesmentioning

confidence: 99%

“…1 This observation allows the systematic derivation of late-time correlators in dS from the Fourier transform of boundary correlators in AdS, which are simpler to obtain and, in many cases, already known. This in particular includes correlators involving scalars and totally symmetric fields of arbitrary integer spin, for which there are few results available to date in de Sitter, where in AdS the complete kinematic map between bulk cubic couplings for any triplet of spinning fields and boundary three-point conformal structures has been worked out explicitly [43]. 1 The relation between correlators in AdS and dS through analytic continuation has been considered in previous works [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bootstrapping inflationary correlators in Mellin space

Sleight

Taronna

2020

Self Cite

199

293

We develop a Mellin space approach to boundary correlation functions in anti-de Sitter (AdS) and de Sitter (dS) spaces. Using the Mellin-Barnes representation of correlators in Fourier space, we show that the analytic continuation between AdS d+1 and dS d+1 is encoded in a collection of simple relative phases. This allows us to determine the late-time tree-level three-point correlators of spinning fields in dS d+1 from known results for Witten diagrams in AdS d+1 by multiplication with a simple trigonometric factor. At four point level, we show that Conformal symmetry fixes exchange four-point functions both in AdS d+1 and dS d+1 in terms of the dual Conformal Partial Wave (which in Fourier space is a product of boundary three-point correlators) up to a factor which is determined by the boundary conditions. In this work we focus on late-time four-point correlators with external scalars and an exchanged field of integer spin-. The Mellin-Barnes representation makes manifest the analytic structure of boundary correlation functions, providing an analytic expression for the exchange four-point function which is valid for general d and generic scaling dimensions, in particular massive, light and (partially-)massless fields. It moreover naturally identifies boundary correlation functions for generic fields with multivariable Meijer-G functions. When d = 3 we reproduce existing explicit results available in the literature for external conformally coupled and massless scalars. From these results, assuming the weak breaking of the de Sitter isometries, we extract the corresponding correction to the inflationary three-point function of general external scalars induced by a general spin-field at leading order in slow roll. These results provide a step towards a more systematic understanding of de Sitter observables at tree level and beyond using Mellin space methods.

“…One of the outstanding problems is to connect two different approaches to higher spin gravity that are presently pursued: Vasiliev's theory and the quasi-local deformed Fronsdal theory. The latter approach (see [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58] and references therein; see also [59] for a review and more references, and [109][110][111][112][113] for more recent works on the holographic reconstruction of bulk vertices) provides a perturbatively defined deformation of the free Fronsdal action following the Noether procedure supplemented by weak locality conditions -as to ensure well-defined amplitudes built using Green's functions in anti-de Sitter spacetime with proper boundary conditions. Up to quartic order, this approach has so far been yielding holographic correlation functions corresponding to unitary free conformal field theories.…”

Section: Motivationsmentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

216

Abstract:We construct an infinite-dimensional space of solutions to Vasiliev's equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over static higher spin black holes. Each solution is obtained by a large gauge transformation of an all-order perturbatively defined particular solution given in a simple gauge, in which the spacetime connection vanishes, the twistor space connection is holomorphic, and all local degrees of freedom are encoded into the residual twistor space dependence of the spacetime zero-forms. The latter are expanded over two dual spaces of Fock space operators, corresponding to scalar particle and static black hole modes, equipped with positive definite sesquilinear and bilinear forms, respectively. Switching on an AdS vacuum gauge function, the twistor space connection becomes analytic at generic spacetime points, which makes it possible to reach Vasiliev's gauge, in which Fronsdal fields arise asymptotically, by another large transformation given here at first order. The particle and black hole modes are related by a twistor space Fourier transform, resulting in a black hole backreaction already at the second order of classical perturbation theory. We speculate on the existence of a fine-tuned branch of moduli space that is free from black hole modes and directly related to the quasi-local deformed Fronsdal theory. Finally, we comment on a possible interpretation of the higher spin black hole solutions as black-hole microstates.