Constraints on moduli masses in Type IIB orientifold compactifications
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Strings generally exist in more dimensions than we are able to observe. To get back to four-dimensional spacetime, we have to compactify the other dimensions. However, these compactifications typically lead to extra massless fields, the moduli, and we have to give them masses to get a phenomenological effective field theory. This is called moduli stabilization. In this thesis we will focus specifically on type IIB string theory compactified on so-called Calabi-Yau orientifolds. For this theory, the moduli can acquire masses by turning on extra background fields or fluxes. We will calculate the trace of these mass values corresponding to two of these moduli, the axio-dilaton and the complex structure moduli and try to find constraints for this trace. We then find that this can be written in terms of a special metric, called the Hodge metric. We also discuss further constraints on these moduli masses by relating them to the so-called flux number and looking at three special cases for the complex structure moduli space: the case of one complex structure modulus, the case of the complex structure moduli space as an Kähler-Einstein manifold and the case where we look at the boundary of the complex structure moduli space.