Momentum-space conformal blocks on the light cone

Marc Gillioz

doi:10.1007/jhep10(2018)125

Dispersion formulas in QFTs, CFTs and holography

Journal of High Energy Physics ◽

10.1007/jhep05(2021)098 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

David Meltzer

Keyword(s):

Fourier Transform ◽

Correlation Functions ◽

Momentum Space ◽

Conformal Blocks ◽

Dispersion Formula ◽

Space Dispersion

Abstract We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

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Light Cone Singularities and the Asymptotic Behavior of Matrix Elements of Operator Products in Momentum Space

Fortschritte der Physik ◽

10.1002/prop.19730210502 ◽

1973 ◽

Vol 21 (5) ◽

pp. 205-263 ◽

Cited By ~ 3

Author(s):

Fritz Schwarz

Keyword(s):

Asymptotic Behavior ◽

Momentum Space ◽

Light Cone ◽

Matrix Elements

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Light-Cone Singularities and Asymptotic Domains of Momentum Space

Physical Review D ◽

10.1103/physrevd.7.3091 ◽

1973 ◽

Vol 7 (10) ◽

pp. 3091-3104 ◽

Cited By ~ 6

Author(s):

Patrizio Vinciarelli ◽

Peter Weisz

Keyword(s):

Momentum Space ◽

Light Cone

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COLLECTIVE AND RELATIVE VARIABLES FOR MASSLESS FIELDS

International Journal of Modern Physics A ◽

10.1142/s0217751x00001944 ◽

2000 ◽

Vol 15 (29) ◽

pp. 4575-4601 ◽

Cited By ~ 2

Author(s):

L. ASSENZA ◽

G. LONGHI

Keyword(s):

Angular Momentum ◽

Harmonic Analysis ◽

Momentum Space ◽

Light Cone ◽

Massless Field ◽

Canonical Realization ◽

Consistency Constraints ◽

Massless Fields

In this paper, a set of canonical collective and relative variables for a classical relativistic massless field are defined and discussed. The discussion is based on a harmonic analysis on the light-cone in momentum space. It is shown how to avoid a set of consistency constraints which are necessary in the massive case. As a result a canonical separation of the angular momentum in collective and relative parts and a canonical realization of an extended BMS algebra are obtained.

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