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Complete classification of topological insulators (including, e.g., the quantum Hall effect and the quantum spin Hall systems), and superconductors (including, e.g., chiral p-wave SC and the B-phase of 3He). An interacting bosonic model that realizes a topological superconducting phase in three spatial dimensions.

We study the sub-structure of heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler modulus dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this Dterm correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilisation.

The origin and evolution of the largest observable structures in the universe (much larger than entire galaxies); understanding why the expansion of the universe is accelerating. Observational techniques: cosmic microwave background, gravitational lensing and gravity waves.