New non-supersymmetric flux vacua from generalised calibrations

Abstract

Abstract We construct a new class of non-supersymmetric ten-dimensional type II flux vacua, by studying first order differential equations which are deformations of the $$\mathcal{N}$$ = 1 supersymmetry conditions. We do so within the context of Generalised Complex Geometry, where there is a natural interpretation of the $$\mathcal{N}$$ = 1 supersymmetry conditions in terms of calibration conditions for probe D-branes, called D-string, domain-wall or space-filling branes, depending on them wrapping two, three or four non-compact dimensions. We focus on the class of non-supersymmetric vacua violating the D-string calibration condition, and write down their general equations of motion in the language of pure spinors. We solve them for a subclass of vacua, where the deformation of the calibration condition is dictated by the foliated geometry of the internal space. We also construct backgrounds violating both the domain-wall and D-string calibration conditions, generalising the one-parameter DWSB class of backgrounds introduced in Lüst et al. We present several explicit solutions with SU(2) and SU(3) structures, and we investigate briefly their associated low energy effective theories.

Keywords

• Flux Compactifications
• Supersymmetry Breaking
• D-Branes