Is the truncated SU(N) non-Abelian gauge theory in extra dimensions renormalizable?

TL;DR

This paper demonstrates that simple truncations of SU(N) gauge theories in extra dimensions are not renormalizable, challenging previous assumptions and highlighting issues with symmetry breaking and dimensional reduction.

Contribution

It reveals that truncated extra-dimensional SU(N) gauge theories cannot be renormalized, contradicting common beliefs and analyzing the impact of symmetry breaking and rescaling.

Findings

Truncated SU(N) theories are not renormalizable.

Tree level relations cannot withstand quantum corrections.

Symmetry breaking and dimensional reduction cause issues.

Abstract

In this letter we show that in the extra dimension model, contrary to the widely accepted conception, the simply truncated $\phi^4$ and non-Abelian SU(N) Kaluza-Klein theories are not renormalizable, i.e. the tree level relations of the effective theories can not sustain the quantum corrections. The breaking down of the tree level relations of the effective theories can be traced back to several factors: the breaking of the higher dimension Lorentz symmetry and higher dimension gauge symmetry, interactions assumed in the underlying Lagrangians, and the dimension reduction and rescaling procedure.