My project aims at improving the understanding of two crucial issues in string theory, the quantization of strings in flux backgrounds and, closely connected, the AdS/CFT correspondence. In both cases I will address the problem in terms of two-dimensional conformal quantum field theories, (CFTs) which are the basic building blocks of string theory.
In this project I will specifically study CFTs based on Lie supergroups, which are extensions of ordinary groups of symmetries involving fermionic degrees of free dom. Incidentally, the same class of CFTs allows to describe disordered systems at criticality in condensed matter theory and statistical physics, most notably quantum Hall systems.
One of the ultimate goals of string theory is to reproduce the standard mo del of particle physics that describes the real world. By considering string theory in flux backgrounds, which are geometric space-times including certain types of gauge fields (so-called Ramond-Ramond fields), we have been able to come closer to the standard model then ever before.
However, the quantization of strings in Ramond-Ramond backgrounds and the resulting physics are still open problems, which I intend to investigate employing new methods in CFT. The fluxes just mentioned also play a prominent role in the AdS/CFT correspondence, which conjectures an equivalence between string theory on particular space-times called AdS spaces and ordinary non-abelian gauge theories as they occur in QCD.
This means that eventually calculations in a gravity theory (and its stringy quantum corrections) can be used to make statements about the behaviour of elementary particles and vice versa. My work on string quantization in the presence of Ramond-Ramond fluxes will allow to perform additional checks of the conjecture and, moreover, to extract interesting physical consequences.
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