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

TL;DR

This paper investigates the renormalization properties of heterotically deformed CP(N-1) sigma models, revealing an infrared fixed point in the coupling ratio and discussing its potential stability beyond one-loop calculations.

Contribution

It introduces the one-loop beta functions for the deformed model and argues for the all-orders stability of the fixed point at ratio 1/2 in the large-N limit.

Findings

The model is asymptotically free under certain conditions.

A fixed point at ratio 1/2 is identified and argued to be stable.

The fixed point may persist beyond one-loop in the large-N limit.

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 \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.