Deconstructing Conformal Blocks in 4D CFT

Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis; Serone, Marco

doi:10.48550/arxiv.1505.03750

Cited by 9 publications

(25 citation statements)

References 56 publications

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“…Equation ( 40) is a second order differential equation (since we are using the quadratic Casimir) that can be used to compute the full conformal block G ∆l [28]. The leading term in ∆ of equation (40) can be used to find the large ∆ behavior of the conformal block. As it is explained in appendix C.3, in this limit (40) reduces to a first order differential equation for the conformal block that can be solved up to an integration constant.…”

Section: Conformal Block At Large ∆mentioning

confidence: 99%

“…The leading term in ∆ of equation (40) can be used to find the large ∆ behavior of the conformal block. As it is explained in appendix C.3, in this limit (40) reduces to a first order differential equation for the conformal block that can be solved up to an integration constant. Moreover we can fix this constant computing the OPE limit (x 12 , x 34 → 0) of the conformal block.…”

Section: Conformal Block At Large ∆mentioning

confidence: 99%

“…To find h ∞l (r, η) we rewrite (40) in the radial coordinates (10) and use the definitions (11) and (21) to get an equation for h ∆l (r, η). If we consider the leading behavior in ∆ we get a simple differential equation…”

Section: Conformal Block At Large ∆mentioning

confidence: 99%

“…In other cases one has to resort to more indirect methods like, integral representations [29][30][31][32][33][34][35], recursion relations that increase the spin of the exchanged operator [27,36] or efficient series expansions [37,38]. There is also a general method to increase the spin of the external operators using differential operators [26,39,40]. However, this method cannot change the SO(d) representation of the exchanged operator.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Recursion relations for conformal blocks

Penedones

Trevisani

Yamazaki

2016

J. High Energ. Phys.

145

400

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In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension ∆ of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in [1] for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current.

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Section: Conformal Block At Large ∆mentioning

confidence: 99%

Section: Conformal Block At Large ∆mentioning

confidence: 99%

Section: Conformal Block At Large ∆mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Recursion relations for conformal blocks

Penedones

Trevisani

Yamazaki

2016

J. High Energ. Phys.

145

400

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show abstract

“…The understanding of spinning blocks for bulk four point functions has advanced significantly since the early papers on the subject [54][55][56][57]. Subsequent developments include the concept and construction of seed blocks [58][59][60][61], the Calogero-Sutherland approach to spinning blocks [62,63] as well as the introduction of weight shifting operators in [64]. A Lorentzian inversion formula for spinning four-point correlators has also been obtained in [20] through the investigation of light-ray operators.…”

Section: Discussionmentioning

confidence: 99%

A Lorentzian inversion formula for defect CFT

Liendo¹,

Linke²,

Schomerus³

2019

Preprint

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We present a Lorentzian inversion formula valid for any defect CFT that extracts the bulk channel CFT data as an analytic function of the spin variable. This result complements the already obtained inversion formula for the corresponding defect channel, and makes it now possible to implement the analytic bootstrap program for defect CFT, by going back and forth between both channels. A crucial role in our derivation is played by the Calogero-Sutherland description of defect blocks which we review. As first applications we obtain the large-spin limit of bulk CFT data necessary to reproduce the defect identity, and also calculate the bulk data of the twist defect of the 3d Ising model to first order in the -expansion.

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Scalar-vector bootstrap

Rejón-Barrera

Robbins

2016

J. High Energ. Phys.

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Abstract:We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.

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Deconstructing Conformal Blocks in 4D CFT

Cited by 9 publications

References 56 publications

Recursion relations for conformal blocks

Recursion relations for conformal blocks

A Lorentzian inversion formula for defect CFT

Scalar-vector bootstrap

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