Topological phase transitions in Calabi‐Yau compactifications of M‐theory

Abstract

AbstractIn this thesis we construct five‐dimensional gauged supergravity actions which describe flop and conifold transitions in M‐theory compactified on Calabi‐Yau threefolds. While the vector multiplet sector is determined exactly, we use the Wolf spaces $X(1+N) = {{U(1+N,2)}\over{U(1+N) \times U(2)}}$ to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of M2‐branes. After specifying the hypermultiplet sector the actions are uniquely determined by M‐theory. As an application we consider five‐dimensional Kasner cosmologies. Including the dynamics of the winding modes, we find smooth cosmological solutions which undergo flop and conifold transitions. Instead of the usual runaway behavior the scalar fields of these solutions generically stabilize in the transition region where they oscillate around the transition locus. The scalar potential thereby induces short episodes of accelerated expansion in the space‐time.