Flux compactification

Recent work is reviewed 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. In this work it is explained that there is a “landscape” of string/M theory vacua, perhaps containing many candidates for describing real world physics, and arguments are presented for and against this idea. Statistical surveys of the landscape are discussed, as well as 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.

Figure 1

(Color online) Values of $\tau$ for rigid CY flux vacua with $L_{\max }=150$. From 152.

Figure 2

(Color online) The SUSY vacuum number density per unit $\psi$ coordinate volume, on the real $\psi$ axis, for the mirror quintic. From 152.

Figure 3

The toric hypersurfaces with $\chi \ge 0$. The vertical axis is $h^{1,1}+h^{2,1}$, while the horizontal axis is $\chi =2(h^{1,1}-h^{2,1})$. The full set also contains the mirror manifolds obtained from these by taking $\chi \to -\chi$. From 327.