Higher Derivative Gauge theory in d = 6 and the $$ \mathbb{C}{\mathbb{P}}^{\left({N}_f-1\right)} $$ NLSM

Abstract

Abstract We consider the $$ \mathbb{C}{\mathbb{P}}^{\left({N}_f-1\right)} $$ ℂ ℙ N f − 1 Non-Linear-Sigma-Model in the dimension 4 < d < 6. The critical behaviour of this model in the large N f limit is reviewed. We propose a Higher Derivative Gauge (HDG) theory as an ultraviolet completion of the $$ \mathbb{C}{\mathbb{P}}^{\left({N}_f-1\right)} $$ ℂ ℙ N f − 1 NLSM. Tuning mass operators to zero, the HDG in the IR limit reaches to the critical $$ \mathbb{C}{\mathbb{P}}^{\left({N}_f-1\right)} $$ ℂ ℙ N f − 1 . With partial tunings the HDG reaches either to the critical U(N f )-Yukawa model or to the critical pure scalar QED (no Yukawa interactions). We renormalize the HDG in its critical dimension d = 6. We study the fixed points of the HDG in d = 6−2ϵ and we calculate the scaling dimensions of various observables finding a full agreement with the order O(1/N f ) predictions of the corresponding critical models.