M-theory, membrane instantons and T-duality

This thesis studies two independent aspects of M-theory. The focus of Chapter 2 is the phenomenologically promising model of our world which relies on the effective low energy dynamics of M-theory. The interesting background includes a Calabi-Yau 3-fold and an interval with M5-branes inserted at points along it. We obtain the effective potential for the scalars resulting from non-perturbative contributions due to open membrane instantons. We also discuss conditions under which the M5-branes may be attracted to the wall; and the chirality-changing phase transitions induced by an M5-brane hitting the wall.; In Chapter 3 we investigate the interplay between the proper quantization of RR fields in terms of K-theory and the T-duality group, an important subgroup of the U-duality group of M-theory. We pay particular attention to the effects of the topological phases in the supergravity action implied by the K-theoretic formulation of RR fields, and we use these to check the T-duality invariance of the partition function. We find that the partition function is only T-duality invariant when we take into account the T-duality anomalies in the RR sector, the fermionic path integral (including 4-fermi interaction terms), and 1-loop corrections including worldsheet instantons. We also discuss some issues which arise when one attempts to extend these considerations to checking the full U-duality invariance of the theory.