Enhanced supersymmetry from vanishing Euler number

TL;DR

This paper demonstrates that compactifying type IIA string theory on Calabi-Yau threefolds with zero Euler number results in four-dimensional theories with enhanced N=4 supersymmetry, with no perturbative corrections at the two-derivative level.

Contribution

It derives the effective action for SU(2) structure manifolds and shows its consistency with gauged N=4 supergravity, highlighting the special case of vanishing Euler number.

Findings

Effective action consistent with N=4 supergravity.

Absence of perturbative corrections at two-derivative level.

Non-perturbative corrections constrained by N=4 gravitino multiplets.

Abstract

We argue that compactifications on Calabi-Yau threefolds with vanishing Euler number yield effective four dimensional theories exhibiting (spontaneously broken) N=4 supersymmetry. To this end, we derive the low-energy effective action for general SU(2) structure manifolds in type IIA string theory and show its consistency with gauged N=4 supergravity. Focusing on the special case of Calabi-Yau manifolds with vanishing Euler number, we explain the absence of perturbative corrections at the two-derivative level. In addition, we conjecture that all non-perturbative corrections are governed and constrained by the couplings of N=4 massive gravitino multiplets.