On Vacuum Structures and Quantum Corrections in String Theory

Abstract

A key target for fundamental physics remains developing a clear understanding of ultra-violet (UV) limits of Effective Field Theories (EFTs) coupled to gravity. In this context, string theory has emerged as a viable candidate for a UV complete theory of quantum gravity. Its compactifications result in a landscape of string vacua encompassing an immensely rich and diverse structure of EFTs. Extracting reliable low energy information from string compactifications notoriously requires a systematic derivation of corrections to the tree level actions which remains a key challenge. Further, despite astonishing progress in constructing string solutions, locating realistic string vacua with desirable properties in the landscape proves to be a delicate task. The objectives of this thesis are threefold: I) first, to perform an extensive analysis of quantum corrections in string theory; II) second, to create a systematic framework to study geometries and backgrounds for viable string compactifications; and III) third, to assess the attainable EFTs in the context of moduli stabilisa- tion. The synergy of these strategies constitutes an innovative approach towards addressing phenomenological questions in string theory. The first part of this thesis describes progress in deriving corrections to classi- cal string effective actions from multi-dimensional investigations by employing the powerful machinery of string dualities and symmetries. Initially, we investigate the structure of higher derivative terms involving the 3-form G3 in the α′ and string-loop expansion of the ten-dimensional Type IIB effective action. Subsequently, we ex- plore α′ corrections in F-theory compactifications to four dimensions in Ch. 6. Here, we focus on the moduli dependence of perturbative corrections to scalar potentials by performing a dimensional analysis. The second part concerns the development of new techniques to examine large classes of Calabi-Yau (CY) geometries and realising the Standard Model in string compactifications. In a first step, we generate a database of CY orientifolds relevant for N = 1 compactifications to four dimensions in Ch. 7. We further consider non- local D7-tadpole cancellation through Whitney branes which leads to a significant enhancement of the total D3-tadpole as compared to conventional SO(8) stacks of D7-branes on top of O7-planes. Afterwards, Ch. 8 presents a construction of the MSSM in global Type IIB orientifold compactifications. We argue that the Standard Model can be embedded into compact CY geometries as a quiver gauge theory through orientifolded D3-branes at del Pezzo singularities dPn with n ≥ 5 in a framework including moduli stabilisation. In this connection, moduli stabilisation in EFTs obtained from string compactifications remains at the heart of the quest for realistic string vacua. In the third part, we address two major obstacles in this direction. First, we provide novel insights into the general structure of 4D N = 1 F-term scalar potentials at higher orders in the α′ and g_s expansion for arbitrary Hodge numbers h^(p,q). In particular, we systematically include odd axions arising from the reduction of 2-forms (B2, C2) in Type IIB which play a central role in string cosmology. Secondly, we design and apply efficient optimisation methods to search for special vacua that may at the same time reveal hidden structure in the landscape. These considerations bring us closer to finding phenomenologically viable low energy EFTs from string theory.