Causality constraints in conformal field theory

Hartman, Thomas; Jain, Sachin; Kundu, Sandipan

doi:10.1007/JHEP05(2016)099

Title: Causality constraints in conformal field theory

Journal Article · Tue May 17 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP05(2016)099· OSTI ID:1326962

Hartman, Thomas ^[1]; Jain, Sachin ^[1]; Kundu, Sandipan ^[1]

Cornell Univ., Ithaca, NY (United States)

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (Φ)⁴ coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators

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Research Organization:: Cornell Univ., Ithaca, NY (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0014123

OSTI ID:: 1326962

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 5; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 159 works

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