Weigand, Timo (2006): Compactifications of the Heterotic String with Unitary Bundles. Dissertation, LMU München: Faculty of Physics 

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Abstract
In this thesis we investigate a large new class of fourdimensional supersymmetric string vacua defined as compactifications of the $E_8 \times E_8$ and the $SO(32)$ heterotic string on smooth CalabiYau threefolds with unitary gauge bundles and heterotic fivebranes. This opens up the way for phenomenologically interesting string compactifications on simply connected manifolds in that the conventional gauge symmetry breaking via Wilson lines is replaced by the embedding of nonflat line bundles into the tendimensional gauge group. The first part of the thesis discusses the implementation of this idea into the $E_8 \times E_8$ heterotic string. After specifying a large class of group theoretic embeddings featuring unitary bundles, we analyse the effective fourdimensional ${\cal N}=1$ supergravity upon compactification. The simultaneous presence of fivebranes and abelian gauge groups requires the introduction of new anomaly cancelling counter terms into the effective action. These are also derived by an Mtheory computation. The full set of GreenSchwarz terms allows for the extraction of the threshold corrections. From the gauge invariant K\"ahler potential for the moduli fields we derive a modification of the FayetIliopoulos Dterms arising at oneloop in string perturbation theory. From this we conjecture a oneloop deformation of the Hermitian YangMills equation and introduce the idea of $\lambda$stability as the perturbatively correct stability concept generalising the notion of Mumford stability valid at treelevel. We then proceed to a definition of $SO(32)$ heterotic vacua with unitary gauge bundles in the presence of heterotic fivebranes and find agreement of the resulting spectrum with the Sdual framework of Type I/Type IIB orientifolds. A similar analysis of the effective fourdimensional supergravity is performed. Further evidence for the proposed oneloop correction to the stability condition is found by identifying the heterotic corrections as the Sdual of the perturbative part of $\Pi$stability as the correct stability concept in Type IIB theory. After reviewing the construction of holomorphic stable vector bundles on elliptically fibered CalabiYau manifolds via spectral covers, we provide semirealistic examples for $SO(32)$ heterotic vacua with PatiSalam and MSSMlike gauge sectors. These can be viewed, by Sduality, as the generalisation of toroidal magnetized $D9$branes to nonabelian braneworlds on genuine CalabiYau manifolds. We finally discuss the construction of realistic vacua with flipped $SU(5)$ GUT and MSSM gauge group within the $E_8 \times E_8$ framework, based on the embedding of line bundles into both $E_8$ factors. Some of the appealing phenomenological properties of this stringy realisation of flipped $SU(5)$ models, in particular stability of the proton, are discussed. MSSMlike gauge coupling unification is possible for the threshold corrected gauge couplings. We explicitly construct a couple of supersymmetric string vacua in both setups with precisely the three observed chiral matter generations and without any exotic chiral states.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  Theoretical Physics, String Theory, Heterotic String, Model Building 
Subjects:  600 Natural sciences and mathematics > 530 Physics 600 Natural sciences and mathematics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  14. July 2006 
1. Referee:  Lüst, Dieter 
Persistent Identifier (URN):  urn:nbn:de:bvb:1955393 
MD5 Checksum of the PDFfile:  accb7e5ab4985a826813cf049c482f2c 
Signature of the printed copy:  0001/UMC 15505 
ID Code:  5539 
Deposited On:  25. Jul 2006 
Last Modified:  19. Jul 2016 16:20 