Projectors and seed conformal blocks for traceless mixed-symmetry tensors

We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic representation of the Lorentz group. The recipe yields the explicit structures in embedding space, and can be applied to any correlator of local operators, with or without a defect. We then focus on the two-point function of traceless symmetric primaries in the presence of a conformal defect, and explain how to compute the conformal blocks. In particular, we illustrate various techniques to generate the bulk channel blocks either from a radial expansion or by acting with differential operators on simpler seed blocks. For the defect channel, we detail a method to compute the blocks in closed form, in terms of projectors into mixed symmetry representations of the orthogonal group.

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“…The seed three point functions saturate the first of the three conditions (39). The requirement (41) matches the one obtained in [32].…”

Section: Three-point Functionssupporting

confidence: 74%

“…This makes the formula convenient for generic integer l, and even suggests its analytic continuation to real values. Moreover, in all the known cases the functions P n l 1 ,...,l k take the form [32] P n l 1 ,...,l k (X 1 , . .…”

Section: Projectors Onto Representations Of So(n)mentioning

confidence: 99%

Spinning operators and defects in conformal field theory

Lauria

Meineri

Trevisani

2019

J. High Energ. Phys.

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“…Even though there can be additional exchange channels involving mixed tensor fields (see e.g. [24][25][26]), we leave the detailed holographic analysis to the future work.…”

Section: Jhep05(2017)070 3 Spinning Three Point Functions and Conformmentioning

confidence: 99%

Anatomy of geodesic Witten diagrams

Chen

Kuo

Kyono

2017

J. High Energ. Phys.

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Abstract:We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.

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“…We cast our discussion in terms of the embedding space formalism [11,16,[45][46][47] throughout. Other recent work on spinning conformal blocks can be found in [31,32,[48][49][50][51][52][53][54][55][56][57][58][59].…”

Section: Jhep11(2017)060mentioning

confidence: 99%

Spinning geodesic Witten diagrams

Dyer¹,

Freedman²,

Sully³

2017

J. High Energ. Phys.

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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.

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Projectors and seed conformal blocks for traceless mixed-symmetry tensors

Cited by 87 publications

References 43 publications

Spinning operators and defects in conformal field theory

Spinning operators and defects in conformal field theory

Anatomy of geodesic Witten diagrams

Spinning geodesic Witten diagrams

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