Dependence of SU(N) coupling behavior on the size of extra dimensions

TL;DR

This paper investigates how SU(N) gauge couplings at high energies are affected by the size of extra dimensions, revealing logarithmic and linear dependencies and patterns influenced by fermion types in both flat and warped geometries.

Contribution

It provides a detailed analysis of gauge coupling evolution considering the size of extra dimensions and Kaluza-Klein modes, including flat and warped geometries.

Findings

Gauge couplings depend logarithmically on extra dimension size in flat geometry.

Gauge couplings show linear dependence on Kaluza-Klein modes.

Patterns vary with bulk and brane fermion flavors.

Abstract

Coupling constants at high energy scales are studied in SU(N) gauge theory with distinct sizes of extra dimensions. We present the solution of gauge couplings as functions of the energy in such a way as to track the number of Kaluza-Klein modes. In a flat extra dimension, it is shown that the gauge couplings have logarithmic dependence on the size of the extra dimension and linear dependence on the number of Kaluza-Klein modes. We find some patterns of the dependence on flavor of bulk and brane fermions. Dependence of gauge couplings on the size of an extra dimension is discussed also in a warped extra dimension.