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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.

Cosmology as a natural meeting ground for fundamental theory (e.g. superstring theory or quantum gravity) and observations. Exploring how seeds laid down in the very early universe developed into the large scale structure we observe in the universe today.

Many aspects of string theory, ranging from its mathematical structure and various formulations, to possible implications for black holes and cosmology. Using string phenomenology to connect theory with reality, i.e. string mathematics with elementary particle physics.

Applications of the quantum nature of our universe to potential new technologies like quantum cryptography and quantum computation. In particular, theoretical developments such as fault-tolerant quantum codes and protocols for quantum error correction.

Observational cosmology, with particular focus on the formation and evolution of large scale structures in our universe like clusters of galaxies as large as 500 million light years. “Weighing” the universe, and mapping out the mysterious dark matter it contains.