Flux compactifications in string theory: A Comprehensive review

http://cds.cern.ch/record/994225/files/0610327.pdf

Four-dimensional string compactifications with D-branes, orientifolds and fluxes

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking

Flux Compactification

Let G be an inner form of a general linear group over a non-archimedean local field. We prove that the local Langlands correspondence for G preserves depths. We also show that the local Langlands correspondence for inner forms of special linear groups preserves the depths of essentially tame Langlands parameters.

Progress in Mathematics

We present an explicit calculation of the spectrum of a general class of string models, corresponding to Calabi-Yau flux compactifications with h1,2 > h1,1 > 1 with leading perturbative and non-perturbative corrections, in which all geometric moduli are stabilised as in [14]. The volume is exponentially large, leading to a range of string scales from the Planck mass to the TeV scale, realising for the first time the large extra dimensions scenario in string theory. We provide a general analysis of the relevance of perturbative and non-perturbative effects and the regime of validity of the effective field theory. We compute the spectrum in the moduli sector finding a hierarchy of masses depending on inverse powers of the volume. We also compute soft supersymmetry breaking terms for particles living on D3 and D7 branes. We find a hierarchy of soft terms corresponding to `volume dominated' F-term supersymmetry breaking. F-terms for Kahler moduli dominate both those for dilaton and complex structure moduli and D-terms or other de Sitter lifting terms. This is the first class of string models in which soft supersymmetry breaking terms are computed after fixing all geometric moduli. We outline several possible applications of our results, both for cosmology and phenomenology and point out the differences with the less generic KKLT vacua.

http://iopscience.iop.org/article/10.1088/1126-6708/2005/08/007/pdf

Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking

Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings

Topological constraints on stabilized flux vacua

We develop means of computing exact degeneracies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of P1's. As explicit examples we consider local P2, P1 × P1 and Ak type ALE space times C. At large N the D-brane partition function factorizes as a sum over squares of chiral blocks, the leading one of which is the topological closed string amplitude on the Calabi-Yau. This is in complete agreement with the recent conjecture of Ooguri, Strominger and Vafa.

https://iopscience.iop.org/article/10.1088/1126-6708/2006/12/018/pdf

Branes, black holes and topological strings on toric Calabi-Yau manifolds

Geometric interpretation of the large N=4 index

We develop means of computing exact degerenacies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of P^1's. As explicit examples we consider local P^2, P^1 x P^1 and A_k type ALE space times C. At large N the D-brane partition function factorizes as a sum over squares of chiral blocks, the leading one of which is the topological closed string amplitude on the Calabi-Yau. This is in complete agreement with the recent conjecture of Ooguri, Strominger and Vafa.

Natalia Saulina

Papers

Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings

Topological constraints on stabilized flux vacua

Branes, black holes and topological strings on toric Calabi-Yau manifolds

Geometric interpretation of the large N=4 index

Branes, Black Holes and Topological Strings on Toric Calabi-Yau Manifolds