The renormalization group flow in 2D N=2 SUSY Landau-Ginsburg models

TL;DR

This paper studies the renormalization group flow in 2D N=2 supersymmetric Landau-Ginzburg models, analyzing field renormalizations and proposing a nonrenormalization theorem in a specific approximation.

Contribution

It introduces a formulation of the nonrenormalization theorem applicable to 2D N=2 SUSY Landau-Ginzburg models and demonstrates its validity at the lowest nontrivial order.

Findings

Chiral fields do not get renormalized at the lowest order

The beta function remains unchanged in the approximation

Nonrenormalization theorem holds at the lowest nontrivial order

Abstract

We investigate the renormalization of N=2 SUSY L-G models with central charge $c=3p/(2+p)$ perturbed by an almost marginal chiral operator. We calculate the renormalization of the chiral fields up to $gg{^*}$ order and of nonchiral fields up to $g(g^{*})$ order. We propose a formulation of the nonrenormalization theorem and show that it holds in the lowest nontrivial order. It turns out that, in this approximation, the chiral fields can not get renormalized $\Phi^{k}=\Phi^{k}_{0}$. The $\beta$ function then remains unchanged $\beta=\epsilon gr$.