Anomalies in N=2 supersymmetric non-linear sigma models on compact Kahler Ricci-flat target spaces

TL;DR

This paper investigates the renormalisability of N=2 supersymmetric non-linear sigma models on compact Kahler Ricci-flat spaces, revealing an unexpected anomaly candidate in the Ricci-flat case.

Contribution

It provides a cohomological analysis showing the presence of an anomaly candidate in Ricci-flat target spaces, challenging previous assumptions.

Findings

Anomaly candidate identified in Ricci-flat cases.

Anomaly candidate disappears in homogeneous Kahler cases.

Uses algebraic, regularisation independent cohomological methods.

Abstract

We analyse with the algebraic, regularisation independent, cohomological B.R.S. methods, the renormalisability of torsionless N=2 supersymmetric non-linear sigma models built on Kahler spaces. Surprisingly enough with respect to the common wisdom, we obtain an anomaly candidate, at least in the compact Ricci-flat case. In the compact homogeneous Kahler case, as expected, the anomaly candidate disappears.