Pseudo-local Theories: A Functional Class Proposal

TL;DR

This work addresses locality in theories with infinitely many derivatives by proposing a functional-class framework based on jet-space and inverse limits to define admissible pseudo-local redefinitions. It introduces $J^ ext{∞}$ and $Q_ ext{∞}$ to classify pseudo-local functionals and develops an unfolding-inspired, cohomological approach to current interactions, separating canonical (local) pieces from pseudo-local improvements. The authors test the framework on string-theory cubic vertices and AdS/CFT-related current constructions, including explicit decompositions into local basis currents and improvement tails, and they analyze quartic couplings to identify potential obstructions to strict locality. They further connect bulk locality to boundary CFT observables via Mellin amplitudes, showing how a locality criterion—namely the commutation of infinite derivative tails with AdS integration—emerges naturally in holographic checks. Overall, the paper provides a principled way to discuss pseudo-locality in higher-spin and tensionless-string contexts and lays groundwork for rigorous quartic locality analyses in HS/CFT dualities.

Abstract

In this article, using the language of jet space, we propose a functional class space for pseudo-local functionals. We test this functional class proposal in a number of examples ranging from string-field-theory to AdS/CFT dualities. Implications of the locality proposal at the quartic order are also discussed.