The Quantum Geometry of N=(2,2) Non-Linear Sigma-Models

TL;DR

This paper explores the geometric structure of N=(2,2) supersymmetric non-linear sigma-models, deriving conditions for UV finiteness and analyzing the role of semi-chiral superfields in the superspace formulation.

Contribution

It provides a comprehensive analysis of the conditions for UV finiteness in N=(2,2) sigma-models, especially highlighting the impact of semi-chiral superfields.

Findings

Derived conditions for one-loop UV finiteness using superspace techniques.

Clarified the geometric implications of semi-chiral superfields.

Connected the formalism to the description of N=(2,2) strings.

Abstract

We consider a general N=(2,2) non-linear sigma-model in (2,2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields. Using superspace techniques, we derive the conditions the potential has to satisfy in order to be ultra-violet finite at one loop. We pay particular attention to the effects due to the presence of semi-chiral superfields. A complete description of N=(2,2) strings follows from this.