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Meyer, René (2009): Holography in External Fields and in Time Dependent Backgrounds. Dissertation, LMU München: Faculty of Physics
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Abstract

Holographic models, i.e. theories describing higher-dimensional gravitational physics in terms of lower-dimensional models without gravitation and vice versa, come in two guises in string theory: The AdS/CFT-Correspondence reformulates strongly coupled nonabelian field theories in terms of weakly coupled gravity theories on Anti-de Sitter space-times, thus allowing studies of strongly coupled gauge theory dynamics. On the other hand, eleven-dimensional quantum gravity (M-theory) can be reformulated in terms of matrix models, field theories of matrix-valued degrees of freedom in 0+1 dimensions. This thesis is concerned with both aspects of holography in string theory: In chapter 3, a way of holographically introducing constant electric and magnetic background fields in the D3-D7 model of holographic quarks is laid out. Magnetic background fields are found to induce spontaneous chiral symmetry breaking, while electric fields induce a vacuum instability which can be interpreted in terms of Schwinger pair production of quark-antiquark pairs. Chapter 4 of this thesis is concerned with the introduction of holographic Fayet-Iliopoulos terms in the D3-D7 model, which lead to spontaneous breaking of supersymmetry and gauge symmetry. The holographic dual of the N=2 Fayet-Iliopoulos term, a particular mode of the Kalb-Ramond field, is identified. Chapter 5 of this thesis is concerned with matrix models in the Friedmann-Robertson-Walker universe: A bosonic matrix model in this particular background is derived for a general scale factor, and the emergence of space-time away from cosmological singularities is shown by a semiclassical argument. An in-depth introduction into string theory, holography, and the AdS/CFT correspondence can be found in chapter 2, while chapter 1 and 6 respectively contain a general introduction and a discussion of the results of this thesis.