All orders analysis of three dimensional CP^(N-1) model in 1/N-expansion

TL;DR

This paper proves the renormalizability of the three-dimensional supersymmetric CP^(N-1) model to all orders in 1/N, demonstrating a non-trivial UV fixed point and no higher order corrections to the beta function.

Contribution

It provides a comprehensive all-orders analysis of the renormalizability and beta function of the supersymmetric CP^(N-1) model in three dimensions using 1/N-expansion.

Findings

All divergences are renormalized by coupling and wavefunction adjustments.

The beta function has no higher order corrections in 1/N.

The model exhibits a non-trivial ultraviolet fixed point.

Abstract

The renormalizability of the three dimensional supersymmetric CP^(N - 1) model is discussed in the 1/N-expansion method, to all orders of 1/N. The model has N copies of the dynamical field and the amplitudes are expanded in powers of 1/N. In order to see the effects of supersymmetry explicitly, Feynman rules for superfields are used. All divergences in amplitudes can be eliminated by the renormalizations of the coupling constant and the wavefunction of the dynamical field to all orders of 1/N. The beta function of the coupling constant is also calculated to all orders of 1/N. It is shown that this model has a non-trivial ultraviolet fixed point. The beta function is shown to have no higher order correction in the 1/N-expansion.