Flux Compactification - 2

Becker-Becker-Schwarz say in the discussion of references to their chapter on flux compactifications:

Flux compactifications were introduced in Strominger (1986) and De Wit,
Smith and Hari Dass (1987) as a generalization of conventional Calabi–Yau
compactifications. Such compactifications include a warp factor, so that the

ten-dimensional metric is no longer a direct product of the external and in-
ternal space-time. No-go theorems implied that in most cases such theories

reduce to ordinary Calabi–Yau compactifications. However, with the devel-
opment of nonperturbative string theory and M-theory, it became evident

that the no-go theorems could be circumvented. Flux compactifications were
first studied in the context of M-theory in Becker and Becker (1996) and in
the context of F-theory in Dasgupta, Rajesh and Sethi (1999). Giddings,
Kachru and Polchinski (2002) explained how flux compactifications can give
a large hierarchy of scales. Grana ̃ (2006) reviews flux compactifications.

 

I have said a few words about Strominger (1986) earlier. Next I intend to take up De Wit, Smith and Hari Dass (1987).

Flux Compactification - 1

 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.