Abstract
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 $(\partial\phi)^4$ coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.
Highlights
Quantum field theories that appear to have causal propagation in vacuum can violate causality in nontrivial states
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
Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators
Summary
Quantum field theories that appear to have causal propagation in vacuum can violate causality in nontrivial states. A version of our position-space optical theorem holds for the correlation functions of non-conformal quantum field theories This relates the lightcone limit to a Regge-like limit in any relativistic QFT, at least in principle, but it remains to be seen whether any of the contributions can be calculated without conformal symmetry. Causality (or analyticity) dictates that certain interactions come with a fixed sign, most notably (∂φ) in a scalar theory with a shift symmetry [1] This can be translated, by the above technology, into a constraint on CFT data, but there was previously no direct CFT derivation. We do not derive any actual bounds for external spinning operators, but we do discuss the structure of the expected constraints This philosophy parallels recent developments in 3d gravity/2d CFT, where the conjecture (1.4) is trivial on the plane (due to Virasoro symmetry) but nontrivial at higher genus.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
