Renormalizability of gauge theories in extra dimensions

TL;DR

This paper investigates the nonperturbative renormalizability of gauge theories in higher dimensions, proposing a scenario based on asymptotic safety that predicts a critical dimension near five, beyond which renormalizability is not possible.

Contribution

It introduces a scenario for gauge theories in extra dimensions using asymptotic safety and calculates the critical dimension where renormalizability ceases to exist.

Findings

Critical dimension for SU(N) gauge theories is near five dimensions.

Renormalizability is excluded for D ≥ 6 dimensions.

A non-Gaussian UV fixed point enables renormalizability in D ≤ D_cr.

Abstract

We analyze the possibility of nonperturbative renormalizability of gauge theories in D > 4 dimensions. We develop a scenario, based on Weinberg's idea of asymptotic safety, that allows for renormalizability in extra dimensions owing to a non-Gaussian ultraviolet stable fixed point. Our scenario predicts a critical dimension D_cr beyond which the UV fixed point vanishes, such that renormalizability is possible for D <= D_cr. Within the framework of exact RG equations, the critical dimension for various SU(N) gauge theories can be computed to lie near five dimensions: 5 ~< D_cr < 6. Therefore, our results exclude nonperturbative renormalizability of gauge theories in D=6 and higher dimensions.