Possible explanations for fine-tuning of the universe

TL;DR

This paper explores the equivalence between the Froggatt-Nielsen mechanism and multi-local field theory in explaining universe fine-tuning, linking these theories to fundamental physics like string theory and the IIB matrix model.

Contribution

It demonstrates the equivalence of two different theoretical approaches to universe fine-tuning and connects them to fundamental physics frameworks.

Findings

Froggatt-Nielsen mechanism is analogous to statistical mechanics.

Multi-local field theory can be derived from Planck/String scale physics.

The IIB matrix model exemplifies the origin of multi-local theories.

Abstract

The Froggatt-Nielsen mechanism and the multi-local field theory are interesting and promising candidates for solving the naturalness problem in the universe. These theories are based on the different physical principles: The former assumes the micro-canonical partition function $\int {\cal{D}}\phi\ \prod_i \delta (S_i^{}-I_i^{})$, and the latter assumes the partition function $\int {\cal{D}}\phi\ \exp\left(iS_M^{}\right)$ where $S_M^{}$ is the multi-local action $\sum_i c_i^{}S_i^{}+\sum_{i,j}c_{i,j}^{}S_i^{}S_j^{}+\cdots $. Our main purpose is to show that they are equivalent in the sense that they predict the same fine-tuning mechanism. In order to clarify our argument, we first study (review) the similarity between the Froggatt-Nielsen mechanism and statistical mechanics in detail, and show that the dynamical fine-tuning in the former picture can be understood completely in the same way as the determination of the temperature in the latter picture. Afterward, we discuss the multi-local theory and the equivalence between it and the the Froggatt-Nielsen mechanism. Because the multi-local field theory can be obtained from physics at the Planck/String scale, this equivalence indicates that the micro-canonical picture can also originate in such physics. As a concrete example, we also review the IIB matrix model as an origin of the multi-local theory.