On the N = 2 supersymmetric CP(N) sigma model and Chern Simons terms

We use the large $N$ self consistency method to compute the critical exponents of the fields and coupling of the supersymmetric CP(N) sigma model at leading order in $1/N$ in various dimensions. We verify that the correction to the critical beta-function slope vanishes at O(1/N) which is consistent with supersymmetry. The three dimensional model is investigated explicitly when a Chern Simons term is included supersymmetrically. We determine the modification that this has on the gauge independent quantity \beta^\prime(g_c) as a function of the Chern Simons coupling, \vartheta. For an N = 2 supersymmetric Chern Simons term the exponent is independent of \vartheta at O(1/N), whilst it is invariant under \vartheta \rightarrow 1/\vartheta when an N = 1 supersymmetric Chern Simons term is included.