Causality, Analyticity and an IR Obstruction to UV Completion

TL;DR

The paper demonstrates that certain low-energy effective field theories with specific sign conditions cannot be embedded in UV-complete theories satisfying analyticity, linking IR superluminality to fundamental non-locality and constraining models like DGP gravity.

Contribution

It reveals a fundamental IR obstruction to UV completion based on analyticity constraints, connecting superluminal fluctuations to the signs of irrelevant operators in effective theories.

Findings

Negative sign operators lead to superluminal fluctuations.

IR breakdown of effective theories indicates non-locality.

Constraints exclude certain models like DGP from UV completion.

Abstract

We argue that certain apparently consistent low-energy effective field theories described by local, Lorentz-invariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the "wrong" signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.