Perturbative Aspects of Heterotically Deformed CP(N-1) Sigma Model. I

Abstract

In this paper we begin the study of renormalizations in the heterotically deformed N=(0,2) CP(N-1) sigma models. In addition to the coupling constant g^2 of the undeformed N=(2,2) model, there is the second coupling constant γdescribing the strength of the heterotic deformation. We calculate both βfunctions, β_g and β_γat one loop, determining the flow of g^2 and γ. Under a certain choice of the initial conditions, the theory is asymptotically free. The βfunction for the ratio ρ=γ^2/g^2 exhibits an infrared fixed point at ρ={1}{2}. Formally this fixed point lies outside the validity of the one-loop approximation. We argue, however, that the fixed point at ρ={1}{2} may survive to all orders. The reason is the enhancement of symmetry - emergence of a chiral fermion flavor symmetry in the heterotically deformed Lagrangian - at ρ={1}{2}. Next we argue that β_ρformally obtained at one loop, is exact to all orders in the large-N (planar) approximation. Thus, the fixed point at ρ= {1}{2} is definitely the feature of the model in the large-N limit.