Nontrivial RR two-form field strength and SU(3)-structure

TL;DR

This paper investigates how nontrivial RR two-form fields and dilaton configurations influence supersymmetry conditions on six-dimensional manifolds, revealing new geometric structures and explicit torsion characterizations.

Contribution

It derives generalized monopole and Killing spinor equations under these conditions and explicitly determines the intrinsic torsion of SU(3)-structures in supersymmetric backgrounds.

Findings

Manifold is Kähler if F_0^{(1,1)}=0.

Explicit intrinsic torsion of SU(3)-structure is obtained.

Conditions for supersymmetry with nontrivial RR fields are characterized.

Abstract

We discuss how in the presence of a nontrivial RR two-form field strength and nontrivial dilaton the conditions of preserving supersymmetry on six-dimensional manifolds lead to generalized monopole and Killing spinor equations. We show that the manifold is K\"ahler in the ten-dimensional string frame if F_0^{(1,1)}=0. We then determine explicitly the intrinsic torsion of the SU(3)-structure on six-manifolds that result via Kaluza-Klein reduction from seven-manifolds with G_2-structure of generic intrinsic torsion. Lastly we give explicitly the intrinsic torsion of the SU(3)-structure for an N=1 supersymmetric background in the presence of nontrivial RR two-form field strength and nontrivial dilaton.