Dimensional reduction of higher-point conformal blocks

Hoback, Sarah; Parikh, Sarthak

doi:10.1007/jhep03(2021)187

Cited by 12 publications

(7 citation statements)

References 41 publications

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“…A noteworthy contribution is the anal-JHEP10(2021)160 ysis by Rosenhaus [25], where the author computed a series expansion for the 5-point scalar exchange conformal block in a 5-point function of external scalar operators. Holographic representations of higher-point conformal blocks were constructed in the works [26][27][28], and dimensional reduction formulae for higher-point scalar exchange blocks were recently derived in [29]. In addition, the null polygon limit of multi-point correlators was later explored in [30].…”

Section: Jhep10(2021)160mentioning

confidence: 99%

Recursion relations for 5-point conformal blocks

Poland

Prilepina

2021

J. High Energ. Phys.

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We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

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Section: Jhep10(2021)160mentioning

confidence: 99%

Recursion relations for 5-point conformal blocks

Poland

Prilepina

2021

J. High Energ. Phys.

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“…Afterwards, we conclude in section 7. We note that with this paper the dimensional reduction of higher-point blocks discussed in [31], which assumed the Feynman rules conjecture, is now proven.…”

Section: Jhep10(2022)097mentioning

confidence: 53%

Feynman rules for scalar conformal blocks

Fortin

Hoback

et al. 2022

J. High Energ. Phys.

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We complete the proof of “Feynman rules” for constructing M-point conformal blocks with external and internal scalars in any topology for arbitrary M in any spacetime dimension by combining the rules for the blocks (based on their Witten diagram interpretation) with the rules for the construction of conformal cross ratios (based on the OPE and “flow diagrams”). The full set of Feynman rules leads to blocks as power series of the hypergeometric type in the conformal cross ratios. We then provide a proof by recursion of the Feynman rules which relies heavily on the first Barnes lemma and the decomposition of the topology of interest in comb structures. Finally, we provide a nine-point example to illustrate the rules.

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“…Other interesting properties of the momentum-space conformal partial wave expansion have to do with the remarkable fact that our results are valid in any space-time dimension d ≥ 3. This would allow to study them in the limit d → ∞ [87,88], or to examine whether recursion relations between various space-time dimensions can be found [89][90][91]. The analyticity in d also implies the ability to study momentum-space correlation functions in non-integer dimensions, where unitarity is known to be broken [92,93].…”

Section: Discussionmentioning

confidence: 99%

Conformal partial waves in momentum space

Gillioz

2021

SciPost Phys.

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The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension d \geq 3d≥3 (including non-integer dd). Each conformal partial wave is expressed as a sum over ordinary spin partial waves, and the coefficients of this sum factorize into a product of vertex functions that only depend on the conformal data of the incoming, respectively outgoing operators. As a simple example, we apply this conformal partial wave decomposition to the scalar box integral in d = 4d=4 dimensions.

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Dimensional reduction of higher-point conformal blocks

Cited by 12 publications

References 41 publications

Recursion relations for 5-point conformal blocks

Recursion relations for 5-point conformal blocks

Feynman rules for scalar conformal blocks

Conformal partial waves in momentum space

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