Asymptotic nonlocality in gauge theories

TL;DR

This paper extends the concept of asymptotic nonlocality from scalar fields to gauge theories, demonstrating how nonlocal scales regulate divergences and exploring potential applications to the Standard Model.

Contribution

It introduces gauge-invariant formulations of asymptotically nonlocal gauge theories and analyzes mass renormalization, highlighting the role of emergent nonlocal scales in divergence regulation.

Findings

Emergent nonlocal scale regulates loop integrals.

Quadratic divergences are suppressed relative to Lee-Wick partners.

Preliminary ideas for extending to non-Abelian theories and the Standard Model.

Abstract

Asymptotically nonlocal field theories represent a sequence of higher-derivative theories whose limit point is a ghost-free, infinite-derivative theory. Here we extend this framework, developed previously in a theory of real scalar fields, to gauge theories. We focus primarily on asymptotically nonlocal scalar electrodynamics, first identifying equivalent gauge-invariant formulations of the Lagrangian, one with higher-derivative terms and the other with auxiliary fields instead. We then study mass renormalization of the complex scalar field in each formulation, showing that an emergent nonlocal scale (i.e., one that does not appear as a fundamental parameter in the Lagrangian of the finite-derivative theories) regulates loop integrals as the limiting theory is approached, so that quadratic divergences can be hierarchically smaller than the lightest Lee-Wick partner. We conclude by making preliminary remarks on the generalization of our approach to non-Abelian theories, including an asymptotically nonlocal standard model.