A.Strominger, Superstrings with Torsion, Nucl.Phys. B274(1986)253
According to Becker-Becker-Schwarz above is one of the two papers that introduced flux compactifications.
In this note I would like to extract the relevant information from the original paper to this effect.
The beginning statement of their abstract is following.
"The conditions for spacetime supersymmetry of the heterotic superstring
in backgrounds with arbitrary metric, torsion, Yang-Mills and dilaton
expectation values are determined using the sigma model approach"
This tells a lot about their task. Then there is the next info: "The equations are shown to agree to leading order in perturbation theory with those derived in a field theory approach, provided one considers a more general ansatz than in previous analyses by allowing for a warp factor".
" Exact solutions with non-zero torsion are found, indicating a new class of finite sigma models".
"Brief comments are made on the implications for phenomenology".
The contents of the paper are as follows: 1. Introduction, 2. Supersymmetry in the Field Theory Approach, 3. Spacetime Supersymmetry in Sigma Model Approach, 4. Solutions, 4.1 Exact Solutions, 4.2 Orbifolds, 4.3 Perturbative Solutions, 4.4 Non-Kahler Manifolds and Flat Directions, 4.5 Discussion, 5. Conclusions
Which part and in what way is the introduction of flux compactifications is something that I shall point out later on.