Asymptotic freedom and higher derivative gauge theories

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 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.

Automated summary

Completing gauge theories with higher derivative terms in the ultraviolet can greatly alter their behavior at high energies. The presence of a large number of derivatives leads to strong interactions, while a low number maintains asymptotic freedom. Consistency issues associated with extra ghosts in higher derivative theories may not affect asymptotically free theories.