Aspects of Wrapped Branes in String and M-Theory
Doctoral thesis, 2009
This thesis consists of an introductory text together with five appended research papers. The Ariadne's thread through the whole thesis is various effects coming from high-dimensional p-branes in various subsectors of string and M-theory.
The low energy effective actions in string and M-theory consists of a classical supergravity together with quantum corrections. In particular the non-perturbative correction terms arise from instanton effects, which are interpreted as p-branes wrapping supersymmetric cycles. The general structure of the full effective action is the result of a complicated interplay between supersymmetry and U-duality. Requiring the action to be invariant under U-duality leads to mathematical functions called automorphic forms. Both perturbative and non-perturbative corrections seem to be captured by these functions. The U-duality groups can be found by analyzing the algebraic structures of the moduli space after toroidal compactification. Using this line of thinking, some simple examples of higher order derivative corrections in pure gravity are investigated.
Compactification on manifolds with special holonomy is also discussed in this thesis, with focus on the resulting moduli spaces. Certain quantum corrections to type IIA string theory compactified on a rigid Calabi-Yau threefold are analyzed.
Manifolds with special holonomy constitute target spaces of the topological subsectors in string and M-theory. The low energy effective action of these theories consists of a classical contribution from a form theory of gravity, which receives quantum corrections from branes wrapping supersymmetric cycles in the target space. In particular the dynamics of the M2- and M5-branes are discussed in the context of a topological version of M-theory.