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

TL;DR

This paper investigates the ultraviolet behavior of a three-dimensional N=4 supersymmetric nonlinear sigma model, demonstrating the cancellation of UV divergences up to next-to-leading order in the 1/N expansion.

Contribution

It provides a detailed analysis of the UV properties of the N=4 SUSY nonlinear sigma model, showing the absence of quantum corrections to the beta function at key orders.

Findings

Beta function has no quantum corrections at leading order.

Beta function has no quantum corrections at next-to-leading order.

UV divergences cancel in the model up to the studied order.

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 $\beta$-function to next-to-leading order and verify that it has no quantum corrections at leading and next-to-leading orders.