Dispersion formulas in QFTs, CFTs and holography

Meltzer, David

doi:10.1007/jhep05(2021)098

Dispersion formulas in QFTs, CFTs and holography

Journal Article · Wed May 12 00:00:00 EDT 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2021)098· OSTI ID:1851483

Meltzer, David ^[1]

California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Institute for Theoretical Physics; California Institute of Technology (CalTech), Pasadena, CA (United States)

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. Atn-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.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632

OSTI ID:: 1851483

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Classification of out-of-time-order correlators Haehl, Felix; Loganayagam, R.; Narayan, Prithvi SciPost Physics, Vol. 6, Issue 1 https://doi.org/10.21468/SciPostPhys.6.1.001	journal	January 2019

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