Wilsonian Renormalization Group Approach to ${\cal N}=2$ Supersymmetric Sigma Models

TL;DR

This paper derives the Wilsonian renormalization group equation for two-dimensional ${ m N}=2$ supersymmetric sigma models, demonstrating asymptotic freedom on compact Einstein K"ahler manifolds and exploring RG flow between different symmetric manifolds.

Contribution

It provides a general derivation of the RG equation for ${ m N}=2$ supersymmetric sigma models, independent of specific K"ahler potentials, and investigates RG flow in models connecting different manifolds.

Findings

Sigma models on compact Einstein K"ahler manifolds are asymptotically free.

The RG equation is derived without dependence on specific K"ahler potentials.

RG flow between manifolds with different symmetries is analyzed.

Abstract

We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This result is gerenal and does not depend on the specific forms of the K\"{a}hler potentials. We also examine the renormalization group flow in a new model which connects two manifolds with different global symmetries.