Asymptotic freedom and higher derivative gauge theories

TL;DR

This paper explores how adding higher derivative terms to gauge theories affects their high-energy behavior, showing that certain configurations can lead to asymptotic freedom and possibly ultraviolet finiteness, with implications for quantum consistency.

Contribution

It identifies conditions under which higher derivative gauge theories remain asymptotically free and potentially ultraviolet finite, addressing ghost-related issues.

Findings

Theories with up to 4 derivatives can be asymptotically free.

Higher derivatives can lead to ultraviolet finite theories.

Ghost masses tend to infinity in the ultraviolet, mitigating associated problems.

Abstract

The ultraviolet completion of gauge theories by higher derivative terms can dramatically change their behavior at high energies. The requirement of asymptotic freedom imposes very stringent constraints that are only satisfied by a small family of higher derivative theories. If the number of derivatives is large enough ($n > 4$) the theory is strongly interacting both at extreme infrared and ultraviolet regimes whereas it remains asymptotically free for a low number of extra derivatives ($n \leqslant 4$). In all cases the theory improves its ultraviolet behavior leading in some cases to ultraviolet finite theories with vanishing $\beta$-function. The usual consistency problems associated to the presence of extra ghosts in higher derivative theories may not harm asymptotically free theories because in that case the effective masses of such ghosts are running to infinity in the ultraviolet limit.