  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 \gamma
describing the strength of the heterotic deformation. We calculate both \beta
functions, \beta_g and \beta_\gamma at one loop, determining the flow of g^2
and \gamma. Under a certain choice of the initial conditions, the theory is
asymptotically free. The \beta function for the ratio \rho =\gamma^2/g^2
exhibits an infrared fixed point at \rho={1}{2}. Formally this fixed point lies
outside the validity of the one-loop approximation. We argue, however, that the
fixed point at \rho ={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 \rho ={1}{2}. Next we argue that
\beta_\rho formally obtained at one loop, is exact to all orders in the large-N
(planar) approximation. Thus, the fixed point at \rho = {1}{2} is definitely
the feature of the model in the large-N limit.

High Energy Physics - Theory