Scheidegger, Emanuel Gilbert (2001): Dbranes on CalabiYau Spaces. Dissertation, LMU München: Faculty of Physics 

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Abstract
In this thesis the properties of Dbranes on Calabi–Yau spaces are investigated. Compactifications of type II string theories on these spaces to which Dbranes are added lead to N = 1 supersymmetric gauge theories on the worldvolume of these Dbranes. Both the Calabi–Yau spaces and the Dbranes have in general a moduli space. We examine the dependence of the gauge theory on the choice of the moduli, in particular those of the K¨ahler structure of the Calabi–Yau manifold. For this purpose we choose two points in this moduli space which are distinguished by the fact that there exists an explicit description of the spectrum of the Dbranes. One of these points corresponds to a manifold in the large volume limit on which the Dbranes are described by classical geometry of vector bundles. At the other points the size of the manifold is smaller than its quantum fluctuations such that the classical geometry looses its meaning and has to be replaced by a conformal field theory. The Witten index in the open string sector is independent of the variation of these moduli and serves, together with mirror symmetry, as a tool to compare the two descriptions. We give an extensive and general presentation of these two descriptions for the class of Fermat hypersurfaces in weighted projective spaces. We explicitly carry out the comparison in many representative examples. Among them are manifolds admitting elliptic and K3fibrations and manifolds whose moduli space can be embedded into the moduli space of another manifold. One main focus is on D4branes, in particular on the dimension of their moduli space. Using the methods developed we are able to further confirm with our results the modified geometric hypothesis by Douglas. It essentially states that the properties of these Dbranes or of these gauge theories can be determined partly by classical geometry, partly by mirror symmetry. A peculiarity of these gauge theories is the appearance of lines of marginal stability at which BPS states can decay. We show the existence of such lines in the framework of this class of Calabi–Yau spaces in two di®erent ways and discuss the connection to the formation of bound states. Of particular interest is the D0brane whose appearance in this framework is explained.
Item Type:  Thesis (Dissertation, LMU Munich) 

Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  9. November 2001 
Persistent Identifier (URN):  urn:nbn:de:bvb:194451 
MD5 Checksum of the PDFfile:  241f58262d7ed29094436f5e1e100149 
Signature of the printed copy:  0001/UMC 11837 
ID Code:  445 
Deposited On:  25. Oct 2002 
Last Modified:  16. Oct 2012 07:31 