Vignettes in string theory : using geometry to probe the worldsheet and strongly coupled physics

Abstract

In this thesis, we construct hybrid linear models in which the chiral anomaly of a gauged linear sigma model is canceled by the classical anomaly of a gauged WZW model. Semi-classically, this corresponds to fibering the WZW model over the naive target space of the sigma model. When the gauge group is abelian, we recover known non-Kahler compactifications; non-abelian models describe novel quasi-geometric flux vacua of the heterotic string. Second, we also investigate sigma models that break world-volume Lorentz invariance. Specifically, we calculate the one loop beta function for a target space metric whose worldvolume scales space and time differently, with dynamical exponent z = 2. We find, as in the isotropic case, the beta function is proportional to the Ricci curvature so that conformal invariance demands Ricci-flatness. We extend this analysis to the case where space and time derivatives come with different target space metrics. We also speculate about coupling the theory to gravity. Finally, we continue the investigation of the recently discovered holographic correspondence between Reissner-Nordstrom black holes in AdS 4 and fermion correlation functions describing Non Fermi Liquids. We numerically study the effects of adding magnetic and electric dipole couplings for the fermions in the bulk. In general, the low energy physics is controlled by an emergent AdS 2 conformal dimension. We find that adding the dipole couplings changes the attainable dimensions. We also find that these couplings can drastically change the locations of fermi surfaces in momentum space.