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'(g(c)) as a function of the Chern-Simons coupling, theta. For an N = 2 supersymmetric Chern-Simons term the exponent is independent of theta at O(1/N), whilst it is invariant under theta --> 1/theta when an N = 1 supersymmetric Chern-Simons term is included.