Singular Fluxes in Ten and Eleven Dimensions : Sources, Singularities, Fluxes and Spam

Abstract: The energy content of our present universe is dominated by the dark-energy, or vacuum energy, which provides accelerated cosmic expansion. Dark energy has a possible effective explanation through a positive cosmological constant. The problem present in any fundamental theory is to explain the underlying dynamics of what gives rise to the cosmological constant.In string theory there are several scenarios that could give insight into what is behind the positive cosmological constant. One such construction uses anti-branes to achieve a net positive energy density of the vacuum. Anti-branes refers in this case to branes placed in a background with oppositely charged flux. As backreaction and localisation procedures are considered for anti-brane constructions a certain kind of singularity arise. This new type of singularity is present in the surrounding flux, which is not directly sourced by the brane.This thesis, and the works contained, considers several aspects of this type of singularity. The first such flux singularity were discovered for the anti-D3-branes, in which the approximations and assumptions of partial smearing and perturbative expansions are used. Included in this thesis are new anti-D6-brane solutions which are placed in oppositely charged flux. It is shown that after the anti-D6-branes are localised, they display the same type of singularity. The strength of this result lies in that it is possible to show the presence of the singularity beyond partial smearing and perturbative expansions. Similar to the anti-D6-brane solutions, new anti-M2-brane solutions are presented. These solutions are also argued to display the same type of singularity.The investigation into the presence of the singularity is just the first step. The second step is to deduce whether this singularity is acceptable and can somehow be resolved. Included in this thesis are two works that considers exactly this. One way of interpreting the singularity is through the absence of a no-force condition between the brane and the surrounding flux. This interpretation leads to the conclusion that the singularity is present due to the use of static Ansätze in a system that is inherently time dependent. Through an adiabatic approach it is here argued that this interpretation leads to a new type of instability.Another way of arguing for a possible resolution of this singularity is whether or not the singularity can be cloaked by an event horizon. This condition have been successful in other systems with singularities. It is argued in this thesis that it is not possible to hide the flux singularity behind a horizon. This leads to one out of two conclusions, either the condition is not a necessary one and the singularity can be resolved in a static manner, or the singularity does not have a resolution.To put these works in context the current singularities from anti-branes program is briefly reviewed to give a full overview of the current situation of these investigations.