Asymptotic nonlocality

Abstract

We construct a theory of real scalar fields that interpolates between two different theories: a Lee-Wick theory with $N$ propagator poles, including $N-1$ 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 $N\to \infty$ 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 $N$) 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-$N$ 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 of this construction in addressing the hierarchy problem.

arXiv comment21 pages LaTeX, 3 figures. Discussion added; $m_1$ now consistently refers to the lightest Lee--Wick mass, with Fig. 1 updated accordingly; v1: 20 pages LaTeX, 3 figures

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