Flux compactification

Abstract

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.Let us briefly discuss the important physical scales in a compactification. Of course, one of the main goals is to explain the observed four dimensional Planck scale, which we denote M P,4 or simply M P . By elementary Kaluza-Klein reduction of D-dimensional supergravity,this will be related to the D-dimensional Planck scale M P,D , and the volume of the compactification manifold Vol(M ). Instead of the volume, let us define the Kaluza-Klein scale M KK = 1/V ol(M ) 1/(D−4) , at which we expect to see Kaluza-Klein excitations; the relation then becomes M 2 P,4 = M D−2 P,D M D−4 KK .(1)In the simplest (or "small extra dimension") picture, used in the original work on string compactification, all of these scales are assumed to be roughly equal. If the Yang-Mills sector is also D-dimensional, this is forced upon us, to obtain an order one four-dimensional gauge coupling; there are other possibilities as well.

Oxidised cosmic acceleration

“…These theorems forbid the presence of warp terms in pure supergravity compactifications, and show that warping is only possible when extended objects with sufficently negative pressure are introduced [11,68]. These extended objects play an essential role in the rich variety of warped compactifications currently under study [100,101,102,103,104,105]. As we have seen in Section 4.2, it is precisely when we have nonzero warping the SEC no-go theorem extends to a NEC no-go theorem for de Sitter cosmologies obtained from curved M. So while introducing extended objects evades the de Sitter SEC no-go theorem, it can lead one afoul of the NEC no-go theorem.…”

“…[100,101,102,103,104,105]). In these constructions a fully explicit higher-dimensional description is not yet available.…”

Nonsupersymmetric flux vacua and perturbed 𝒩 = 2 systems

“…Because x(z) should be locally one-to-one near the marked points, we must construct it from functions with single poles, namely F (1) 1 and F (1) 2 . On the other hand, y(z) ∼ x(z) 2 near the marked points so it must contain functions with double poles, F (2) 1 and F (2) 2 .…”

“…Over the last years much progress has been made in studying flux compactifications in string theory; see [1,2] for recent reviews. By now there is strong evidence that there is a huge number of supersymmetric vacua with negative cosmological constant in which all scalar moduli are stabilized, the so called landscape of string theory.…”

Inflection point inflation and time dependent potentials in string theory

“…In the context of brane inflation this was shown in [8,9,10]. Here we focus on modular inflation in which one of the moduli fields is the inflaton and the other moduli fields are assumed to be stabilized with a higher mass than the characteristic mass scale associated with the inflaton (for a recent review on moduli stabilization see [14]). We consider the case where the inflaton is the radion.…”