Backreaction of Localised Sources in String Compactifications

TL;DR

This work investigates how the backreaction of localised sources in string compactifications affects the four-dimensional effective theory, focusing on the validity of smeared approximations and the role of BPS bounds. It shows that BPS configurations allow localisation with no shift in moduli and that the Douglas–Kallosh problem can be avoided via warping, while non-BPS setups can yield unresolvable flux singularities near branes and challenge simple localisation. A central result is that, in many Type II flux compactifications, the lower-dimensional cosmological constant Λ is determined by the on-shell action of localised sources, with flux contributions often gaugeable away; this enables Λ to be computed from near-source data in a wide range of models, including GKP-like IIB, DGKT, and KKLT-inspired scenarios. The thesis also presents a detailed non-BPS toy model that exhibits a flux singularity not cured by brane polarisation, offering evidence that anti-brane uplifts in warped throats may be unstable or require novel stringy effects for resolution. Overall, the results clarify when smeared approximations are trustworthy and illuminate the difficulties in achieving meta-stable de Sitter vacua in string theory, with explicit connections to KS-type backgrounds and brane polarisation analyses.

Abstract

Localised sources such as D-branes or orientifold planes play an important role in many string compactifications that are relevant for phenomenology. The presence of these objects typically induces complicated dynamics in the compact dimensions such that a full solution to the 10d equations of motion is often out of reach. In order to still be able to make statements about the 4d effective theory arising in the low-energy limit, the equations of motion are usually only solved in an integrated sense, while the backreaction of the localised sources on the internal fields is neglected. This simplification is often referred to as smearing. In this work, we investigate to what extent smearing may affect observables in the effective low-energy theory and whether it may lead to fake solutions that would cease to exist once the backreaction is properly taken into account. We analyse explicit examples for which smeared solutions exist and find that the reliability of the smeared approximation appears to depend on whether or not these solutions saturate a BPS bound. We also address the proposal of placing anti-D3-branes at the tip of a warped throat geometry like the Klebanov-Strassler solution in order to construct meta-stable de Sitter vacua in string theory. We show that, under a few general assumptions, the backreaction of the fully localised anti-branes yields a singularity in fields that do not directly couple to them, and we give an argument suggesting that the singularity is not resolved by brane polarisation. We furthermore demonstrate that, in many string compactifications involving non-trivial background fluxes, the effective lower-dimensional cosmological constant is determined by the on-shell action of the localised sources present in the solution. This often allows to compute the cosmological constant without resorting to potentially unreliable approximations like smearing.

Figures (5)

• Figure 3.1: A smooth brane profile.
• Figure 3.2: A brane profile in the shape of a step function.
• Figure 3.3: An example for a flux configuration in the presence of a step function source with extrema that are required for global tadpole cancellation but forbidden by the constraint $\mathrm{sgn}\, \alpha^{\prime\prime} = \mathrm{sgn}\, \alpha$.
• Figure 3.4: Flux configurations for a setup with $\overline{\textrm{D}6}$-branes on one pole (left picture) and for a setup with $\overline{\textrm{D}6}$-branes on both poles (right picture). Both configurations with BPS boundary conditions, which are excluded due to the requirement of global tadpole cancellation and the constraint $\mathrm{sgn}\, \alpha^{\prime\prime} = \mathrm{sgn}\, \alpha$ that must be fulfilled at every extremum away from the sources.
• Figure 3.5: Flux configurations for a setup with $\overline{\textrm{D}6}$-branes on one pole (left picture) and for a setup with $\overline{\textrm{D}6}$-branes on both poles (right picture). Both configurations with unusual boundary conditions, which are not excluded by the topological argument.