The present thesis contains the development of new techniques to compute the Yukawa couplings for the fundamental matter in the context of string theoretic Brane World Models. Exploiting the' unitarity of String Theory these couplings are derived by means of factorisation of the classical limit of the two-loop twisted partition function in generic toroidal compactifications. In fact by taking the Schwinger time of the strings propagating in the loops to infinity, the string theoretic diagram is reduced to a field theoretic interaction involving the low-lying states of oscillations of the so-called twisted strings. These are strings stretched between two D-Branes either intersecting at angles or with different magnetic fields turned on in their world-volumes and they reproduce four dimensional chiral fermions in the low energy limit of the theory. The models involving intersecting or magnetised D-Branes are related to one another by means ofT-Duality. The factorisat~on of the resulting diagram yields three propagators and two complex conjugate copies of the sought Yukawa couplings, whose moduli dependence (both on the open and on the closed string moduli) is determined in full generality in toroidal compactifications of the models. The actual partition function is computed, by using the conformal properties of String Theory, in the closed string channel, in which it becomes a tree-level interaction between three closed strings ending on magnetised D-Branes. The computation performed is generalised to the case of g+l external states and it corresponds to the g-loop twisted partition function in the open string channel. The fundamental ingredients for the calculation are the Reggeon vertex for the emission of g+ 1 off-shell closed strings and the boundary state fOf a wrapped magnetised D-Brane. A careful analysis of the phase factors involved in determining the form of these objects in toroidal compactifications leads also to a generalisation of the known T -Duality rules.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:504544 |
| Date | January 2008 |
| Creators | Duo, Dario |
| Publisher | Queen Mary, University of London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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