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Abstract
This thesis addresses several problems related to lowenergy supersymmetry and quantum gravity. The first of those is the gauge coupling unication problem within the Minimal Supersymmetric Standard Model. We derive a so called holomorphic master formula which we use in order to analyze the twoloop problem using oneloop renormalization group equations. In terms of modelbuilding our solution relies on the inclusion of extra vectorlike matter at intermediate energies which couples to the two Higgs doublets through Yukawa interactions. We find that the extra Yukawa couplings can ameliorate the twoloop discrepancy, an effect which is encoded in the wavefunction renormalization factors of the Higgs superfields. Next we address and solve the so called muproblem by combining two wellknown mechanisms for generating a muterm in the MSSM superpotential  we add a gauge singlet superfield which acquires a vacuum expectation value in its scalar component, on the one hand, and extra vectorlike messenger superfields which couple directly to the Higgs sector, on the other. A key ingredient of our construction is the nontrivial hierarchy between the soft masses in the Higgs sector which puts our model into the class of models known as lopsided gauge mediation. This so called inverted hierarchy modifies the RG running of the soft singlet mass ensuring that the effective muterm can attain sufficiently large values, i.e. mu > 100 GeV, as required by phenomenology. Finally we discuss an application of the so called functional renormalization group to quantum gravity. We construct a diffeomorphism invariant and gaugefixing independent flow equation which we use in order to analyze the phase diagram of quantum gravity. We solve this equation in several nontrivial approximations, starting with the usual background field approximation. We confirm the presence of a nontrivial UV fixed point and also analyze the infrared sector of the theory which exhibits an infrared fixed point related to classical gravity.
Item Type:  Dissertation 

Supervisor:  Hebecker, Prof. Dr. Arthur 
Date of thesis defense:  11 July 2012 
Date Deposited:  07 Jan 2013 08:16 
Date:  2012 
Faculties / Institutes:  The Faculty of Physics and Astronomy > Institute for Theoretical Physics 
Subjects:  530 Physics 
Controlled Keywords:  Supersymetrie, Renormierungsgruppe 