Masses of moduli in IIB flux compactifications

Abstract

In this thesis we calculate and discuss the mass spectrum of two examples of type IIB flux compactifications. Firstly in the introduction we discuss how string theory leads to higher dimensional spaces, how we can compactify the extra dimensions on an internal manifold creating extra massless modes (moduli) and how fluxes can generate a mass for the moduli. In the last part of the introduction we discuss our setting: four-dimensional N = 1 supergravity. In chapter 2 and 3 we calculate the masses of the moduli for the case with one com- plex structure modulus (h−2,1 = 1), one complex structure modulus in the large-complex- structure limit and two complex structure moduli (h−2,1 = 2). In chapter 4 we discuss certain aspects of the masses we found in chapter 2 and 3. For each case we describe when there can be degeneracies in the masses and we consider the masses in certain limits of moduli space. In chapter 5 we recap and discuss our results. In this thesis we find the following features for the masses of the moduli in the cases we consider: • For a general flux all moduli receive a mass and are stabilized when turning on these fluxes. Only for very specific cases the masses of one or a few of the moduli are zero. • Even having degenerate masses seems to be the exception. For example for all the masses to be equal we need either h0 or hi to vanish such that H = hiχi + hjχj or H = h0Ω + h0Ω. • When going to extremes in the parameters that determine the fluxes the masses approximate degenerate pairs and one pair of masses stays small while the other masses diverge. We note that restricting the options for compactifications on the basis of the moduli masses in these examples is difficult. Possibly these results combined with an analysis of the stabilisation of the K¨

ahler moduli using KKLT [1] would be able to provide more

restrictions.