Abstract
There are effective field theories that cannot be embedded in any UV complete theory. We consider scalar effective field theories, with and without dynamical gravity, in D-dimensional anti-de Sitter (AdS) spacetime with large radius and derive precise bounds (analytically) on the coupling constants of higher derivative interactions ϕ2□kϕ2 by only requiring that the dual CFT obeys the standard conformal bootstrap axioms. In particular, we show that all such coupling constants, for even k ≥ 2, must satisfy positivity, monotonicity, and log-convexity conditions in the absence of dynamical gravity. Inclusion of gravity only affects constraints involving the ϕ2□2ϕ2 interaction which now can have a negative coupling constant. Our CFT setup is a Lorentzian four-point correlator in the Regge limit. We also utilize this setup to derive constraints on effective field theories of multiple scalars. We argue that similar analysis should impose nontrivial constraints on the graviton four-point scattering amplitude in AdS.
Highlights
It is well-known that not all effective field theories (EFTs) can be UV completed
We will address a closely related question: what scalar EFTs in AdSD cannot be embedded into a UV theory that is dual to a CFTD−1 obeying the usual CFT axioms? We will provide a partial answer to this question by leveraging the huge advancement in constraining the space of consistent CFTs from well-established conformal bootstrap axioms
Especially for CFTs that are dual to some EFT in anti-de Sitter (AdS), it is easy to see that a ≥ d since CFT operators that are exchanged are either double trace operators or single trace operators with a = ∆ ≥ d from a bulk three-point interaction
Summary
It is well-known that not all effective field theories (EFTs) can be UV completed. For multiple fields there are interference effects that are constrained by the CFT axioms leading to an infinite set of non-linear bounds among various higher derivative coupling constants.. For multiple fields there are interference effects that are constrained by the CFT axioms leading to an infinite set of non-linear bounds among various higher derivative coupling constants.10 These additional tools will certainly be useful for bounding the four-graviton scattering amplitude in AdS by using the dual CFT description. In appendix A we demonstrate how Rindler positivity in CFT follows from unitarity and crossing symmetry
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