Cancellation of UV Divergences in the N=4 SUSY Nonlinear Sigma Model in Three Dimensions

Abstract

We study the UV properties of the three-dimensional ${\cal N}=4$ SUSY nonlinear sigma model whose target space is $T^*(CP^{N-1})$ (the cotangent bundle of $CP^{N-1}$) to higher orders in the 1/N expansion. We calculate the $β$-function to next-to-leading order and verify that it has no quantum corrections at leading and next-to-leading orders.