Maximal Locality and Predictive Power in Higher-Dimensional, Compactified Field Theories

TL;DR

This paper investigates how optimizing the ultraviolet cutoff in higher-dimensional, compactified scalar field theories can enhance their predictive power, revealing approximate parameter agreement with lower-dimensional effective theories under certain conditions.

Contribution

It demonstrates that maximizing the ultraviolet cutoff in higher-dimensional theories aligns their parameters with lower-dimensional effective theories, supporting increased predictability.

Findings

Infrared parameters in compactified theories approximate uncompactified ones when R^{-1} exceeds a scale s times M.

Maximizing the ultraviolet cutoff enhances the predictive power of nonrenormalizable theories.

The optimal parameter values depend on the dimension D and the compactification radius R.

Abstract

To achieve a maximal locality in a trivial field theory, we maximize the ultraviolet cutoff of the theory by fine tuning the infrared values of the parameters. This optimization procedure is applied to the scalar theory in $D+1$ dimensions ($D \geq 4$) with one extra dimension compactified on a circle with radius $R$. The optimized, infrared values of the parameters are then compared with the corresponding ones of the uncompactified theory in $D$ dimensions, which is assumed to be the low-energy effective theory. We find that these values approximately agree with each other, as long as $R^{-1} \gsim s M$ is satisfied, where $s\simeq 10,50,50, 100$ for $D=4,5,6,7$, and $M$ is a typical scale of the $D$-dimensional theory. This result supports the previously made claim that the maximization of the ultraviolet cutoff in an nonrenormalizable field theory can give the theory more predictive power.