Higher Derivative Gauge theory in d=6 and the C-1(N/-1) NLSM

We consider the CIP(Nf 1) Non -Linear-Sigma-Model in the dimension 4 < d< 6. The critical behaviour of this model in the large Nf limit is reviewed. We propose a Higher Derivative Gauge (HDG) theory as an ultraviolet completion of the CP(Nf 1) NLSM. Tuning mass operators to zero, the HDG in the IR limit reaches to the critical CP(Nf With partial tunings the HDG reaches either to the critical U(Nf)-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 = 6-2 and we calculate the scaling dimensions of various observables finding a full agreement with the order O(1/Nf) predictions of the corresponding critical models.