
TL;DR
This paper develops a theory of scalar fields that smoothly transitions from Lee-Wick models with multiple poles to a nonlocal infinite-derivative theory as the number of poles approaches infinity, offering insights into divergence regulation.
Contribution
It introduces an auxiliary-field formulation that unifies Lee-Wick and nonlocal theories, providing a new framework for addressing quadratic divergences and the hierarchy problem.
Findings
The large-N limit yields a nonlocal infinite-derivative theory.
The effective scale for divergence regulation can be lower than the lightest resonance.
The construction offers potential solutions to the hierarchy problem.
Abstract
We construct a theory of real scalar fields that interpolates between two different theories: a Lee-Wick theory with propagator poles, including Lee-Wick partners, and a nonlocal infinite-derivative theory with kinetic terms modified by an entire function of derivatives with only one propagator pole. Since the latter description arises when taking the limit, we refer to the theory as "asymptotically nonlocal." Introducing an auxiliary-field formulation of the theory allows one to recover either the higher-derivative form (for any ) or the Lee-Wick form of the Lagrangian, depending on which auxiliary fields are integrated out. The effective scale that regulates quadratic divergences in the large- theory is the would-be nonlocal scale, which can be hierarchically lower than the mass of the lightest Lee-Wick resonance. We comment on the possible utility…
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