Daniel is currently working calculating geodesics in moduli spaces of string theory, with aims to develop our understanding of field spaces in quantum gravity and aspects of the Swampland
In this thesis we mainly study two aspects of the weak gravity conjecture (WGC). First, we look at an indirect argument in favor of the WGC based on holographic entropy bounds. We make the existing proposals more precise and relate them to recent work on communication bounds. In the second part, we explain the connection between the WGC and the phenomenon of emergence. Here, we make a precise toy-model calculation and discuss similar observations in String Theory. Most of the relevant formalism and concepts are provided either in the main part of the thesis or in the appendix, hence the > 100 pages.
We study the Weak Gravity Conjecture in the presence of scalar fields. The Weak Gravity Conjecture is a consistency condition for a theory of quantum gravity asserting that for a U(1) gauge field, there is a particle charged under this field whose mass is bounded by its charge. It was extended to a statement about any canonical pair of (p-1)-dimensional object and p-form coupling to it, in particular to axion-instanton pairs. The gauge-scalar Weak Gravity Conjecture is a modification of this bound that includes scalar interactions. We propose a similar extension to cases where scalar fields are present for the axion-instanton Weak Gravity Conjecture and provide evidence from Type IIA supergravity.
This thesis is a study of string theory compactifications to four dimensions and the constraints the Effective Field Theories must exhibit, exploring both the closed and open sectors. In the former case, we focus on axion monodromy scenarios and the impact the backreaction of the energy density induced by the vev of an axion has on its field excursions. For all the cases studied, we find that the backreaction is small up to a critical value, and the proper field distance is flux independent and at most logarithmic in the axion vev. We then move to the open sector, where we use the framework of F-theory. We first explore the relation between the spectra arising from F-theory GUTs and those coming from a decomposition of the adjoint of E8 to $SU(5)\times U(1)^n$. We find that extending the latter spectrum with new SU(5)-singlet fields, and classifying all possible ways of breaking the Abelian factors, all the spectra coming from smooth elliptic fibration constructed in the literature fit in our classification. We then explore generic properties of the spectra arising when breaking SU(5) to the Standard Model gauge group while retaining some anomaly properties. We finish by a study of F-theory compactifications on a singular elliptic fibration via Matrix Factorisation, and find the charged spectrum of two non-Abelian examples.
We study the consistency of super-Planckian scalar field displacements in quantum gravity. The first part of this thesis discusses the cosmology of the early universe and in particular large field inflation, which explains the homogeneous initial conditions. Several models of natural inflation are presented. It is argued that the embedding of these models into a quantum gravity framework can be problematic because of the required super-Planckian scalar field displacements. Concrete obstructions to an implementation in string theory are presented. The second part is devoted to the study of various conjectures on the moduli space of quantum gravity theories which constrain large field displacements. The Weak Gravity Conjecture constrains mass-to-coupling ratios in gauge theories. In string theory these are functions of scalar moduli. We propose a connection between a variant of the Weak Gravity Conjecture and a Swampland Conjecture, which states that as a scalar field displacement asymptotes to infinity an infinite tower of states appears, exponentially light in the displacement. We show that the Weak Gravity Conjecture leads to evidence for this and that the exponential behaviour sets in quickly after the field variation passes the Planck scale. These conjectures can be used to constrain large field inflation models.
One of the challenges in string phenomenology is to find compactifications of superstring theory such that the resulting low-energy effective theory resembles the Minimal Supersymmetric Standard Model of particle physics with its SU(3) × SU(2) × U(1) gauge group, three generations of fermions and one Higgs doublet. An established method that achieves the correct gauge group is to model an SU(5) GUT theory using type IIB superstring theory with D7-branes and then to break the GUT group by including a hypercharge flux. The correct non-perturbative description of type IIB superstring theory with D3- and D7-branes is F-theory. In F-theory, the geometry of the branes and of the compactification space is captured by a four-dimensional elliptically fibered Calabi-Yau. In , the authors give a basic example of a realistic model in this context, including however nine generations of fermions and five Higgs doublets. The aim of this thesis is to review the necessary prerequisites in differential geometry, to explain in detail how such a model in F-theory can be built, and finally to improve the model given in . By including a so-called G4-flux, we were able to reduce the number of generations in the model to the desired value of three.
In this thesis we study heterotic duality of the SU(5)xU(1)xU(1) F-theory models introduced in  in compactifications to four and six dimensions. We investigate the relationship between GUT singlets in the F-theory geometry and singularities in the heterotic compactification. Moreover, we derive constraints on the models as to render the heterotic geometry smooth. In four dimensions, we find that two of the four models do not admit a smooth heterotic dual. We proceed to consider how these singularities are related to possible embeddings of the F-theory spectrum into a Higgsed E8 and show that for the two models allowing for a smooth heterotic geometry, there are multiple embeddings such that all non-singular states are embeddable whereas the singular ones are not. In six dimensions all four models allow for a smooth heterotic dual, but the geometries are severely restricted by said constraints.
The aim of this thesis is to derive the consistent choices for hypercharge flux in the F-Theory GUT models, that were constructed in . Their constraints are imposed by emerging gauge anomalies in four dimensions, so beforehand the chiral anomaly in quantum field theory as well as the the concept of flux is introduced and discussed. Initially, a short review of the representation theory of the standard model and the Georgi-Glashow model of SU(5) grand unification will be given.
In this thesis, the Standard Model and the Higgs Mechanism are presented and their connection to group theory and symmetries is explored. In the following chapter, the SU(5) Georgi-Glashow model is examined as a possible Grand Unified Theory (GUT) that further unifies the concepts introduced in the Standard Model. Advancing after this model, there is an ongoing search for other theories going beyond the Standard Model, possibly unifying all of physics in a ”Theory of Everything”. The most promising candidate for this to date is String Theory, and the rest of the thesis deals with structures called Complete Networks, which find some applications in type IIB String Theory.
This thesis uses and derives the methods for the calculation of the running couplings in the Standard Model of Particle Physics. On the basis of the running couplings for the three gauge couplings and the Higgs quartic coupling, the phenomena of coupling unification and the instability of the electroweak vacuum are discussed in search of potential implications which hint to beyond the Standard Model Physics. For this, the concepts of Supersymmetric Theories and Grand Unification Theories are discussed in comparison to the predictions of the Standard Model. The effect of adding a pair of fermions charged under SU(3) to the Standard Model is calculated to quantify the change of running couplings by postulating additional particles and to relate this to the previous discussion.
palti [at] mppmu.mpg.de
Föhringer Ring 6 D-80805 Munich