Abstract
We consider flux compactifications of heterotic string theory in the presence of fermionic condensates on M 1,2 × X 7 with both factors carrying a Killing spinor. In other words, M 1,2 is either de Sitter, anti-de Sitter or Minkowski, and X 7 possesses a nearly parallel G 2-structure or has G 2-holonomy. We solve the complete set of field equations and the Bianchi identity to order α ′. The latter is satisfied via a non-standard embedding by choosing the gauge field to be a G 2-instanton. It is shown that none of the solutions to the field equations is supersymmetric.
Highlights
Conditions under which the solutions preserve supersymmetry
We solve the complete set of field equations and the Bianchi identity to order α
The gauge field is taken to be a generalized instanton on the internal manifold X7
Summary
In order to simplify the equations of motion, we will assume for the remainder of the paper that the dilation vanishes, i.e. Space-time and spinor factorization. Note that the form of the condensates (2.19) and (2.20) differs crucially from condensates considered previously in compactifications to four-dimensional space-times. In the latter case one may consistently confine the condensate to the compactification space. For future reference we review some aspects of the geometry of maximally symmetric Lorentzian manifolds, i.e. de Sitter, anti-de Sitter and Minkowski spaces. These spaces possess a Killing spinor with Killing number μ1, meaning a spinor ζ satisfying. Note that the curvature only depends on even powers of ρ1 and, the sign of ρ1 will only enter the supersymmetry variations but not the equations of motion
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