On the predictability of string theory
Examensarbete för masterexamen
Physics and astronomy (MPPAS), MSc
Eleven-dimensional supergravity can be compactified on AdS4 M7 where M7 can be chosen as the so called squashed seven-sphere. This allows two solutions, depending on the orientation of the sphere, one with N = 1 supersymmetry and one non-supersymmetric. Both solutions correspond to spontaneous symmetry breakings of the round sphere. However, recent conjectures concerning the string landscape have led to the statement that non-supersymmetric AdS vacua should be unstable. By studying the standard model of particle physics one can make certain predictions about the masses of neutrinos from this conjecture, leading to measureable predictions from string theory. This thesis aims to study the mass spectra of the squashed sphere in order to gain some insight into whether or not any instabilities occur. This could then either disprove or strengthen the proposed conjectures. The full spectrum is not found but some helpful steps along the way have been provided. In particular, only the scalar, vector and spinor spectra are studied. The thesis also discusses some of the conjectures regarding the string landscape in more detail and shows how these can be used to make predictions in particle physics. The concepts of Kaluza-Klein compactification and supersymmetry are also introduced, as well as some group theoretical methods for studying differential operators on manifolds. The full mass spectra of the round seven-sphere are derived using two different methods.
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