## Masses of moduli in IIB flux compactifications

##### Summary

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.