On a possible breaking of global N=2 supersymmetry in non-linear $\si$ models on compact K\"ahler target spaces

TL;DR

This paper investigates the potential breaking of N=2 supersymmetry in non-linear sigma models on compact Kähler spaces, revealing an anomaly candidate linked to the Hodge number h^{3,0} and its dependence on the geometry of the target space.

Contribution

It demonstrates that anomalies in N=2 supersymmetric sigma models depend on the Hodge number h^{3,0}, challenging previous assumptions about their renormalizability.

Findings

Anomaly candidate appears when h^{3,0} ≠ 0, especially in Calabi-Yau spaces.

No anomaly candidate in compact homogeneous Kähler spaces.

The analysis uses algebraic, regularisation independent, cohomological B.R.S. methods.

Abstract

We analyse with the algebraic, regularisation independent, cohomological B.R.S. methods, the renormalisability of torsionless N=2 supersymmetric non-linear $\si$ models built on compact K\"ahler spaces. Surprisingly enough with respect to the common wisdom, we obtain an anomaly candidate, when the Hodge number $h^{3,0}$ of the target space manifold is different from zero : this occurs in particular in the Calabi-Yau case. On the contrary, in the compact homogeneous K\"ahler case, the anomaly candidate disappears.