## Quantum corrections and the Swampland

##### Title (trans.)

Correcciones Cuánticas y el Swampland##### Author

Wiesner, Max##### Advisor

Marchesano, Fernando##### Entity

UAM. Departamento de Física Teórica; Instituto de Física Teórica (IFT)##### Date

2021-09-10##### Funded by

The author received funding from a fellowship from ’la Caixa’ Foundation (ID 100010434) with fellowship code LCF/BQ/DI18/11660033 and from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 713673##### Subjects

Cuerdas, teoría de las; Teoría cuántica; Física##### Note

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 10-09-2021Esta tesis tiene embargado el acceso al texto completo hasta el 10-03-2023

Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

### Abstract

In this thesis, we study string theory compactifications to four dimensions in the context
of the Swampland Program. Our particular focus lies on the role of quantum corrections
for the realisation of certain swampland conjectures in models arising from string theory.
After reviewing some background material on string and F-theory compactifications,
we start by extending the study of the Swampland Distance Conjecture to the hypermultiplet
sector of type IIB string theory compactified on Calabi–Yau three-folds. Unlike its
vector multiplet counterpart, the hypermultiplet moduli space is heavily affected by Dbrane
instantons that yield significant corrections to the effective four-dimensional theory.
We investigate the effect of these D-brane instantons in regions of moduli space that are
classically at infinite distance. For these we show that certain classical infinite distance
singularities are generically obstructed by such quantum effects, which deflect trajectories
approaching the classical infinite distance point towards a weak-coupling point. We further
relate the presence of D-brane instanton corrections to the emergence of tensionless strings.
In that context, we show that, via duality, those infinite distance limits persisting at the
quantum level can be identified with weak-coupling limits for fundamental type II strings
in accordance with the Emergent String Conjecture.
We then move on to consider asymptotic regions in the moduli space of F-theory
compactifications on elliptically fibered Calabi–Yau four-folds. In the Kähler moduli space
we show that limits qualifying as emergent string limits can only be obtained if the base of
the elliptically fibered Calabi–Yau four-fold is itself fibered by either a unique rational or a
unique genus-one curve. In the limit of vanishing fibral volume this gives rise to a unique
emergent heterotic or type II string, respectively. Importantly, an analysis of perturbative
0-corrections to the F-theory moduli space geometry reveals that these precisely censor
classically pathological limits for which the tension of a weakly-coupled heterotic string
would be parametrically below the Kaluza–Klein scale. We further investigate the effect
of the perturbative 0-corrections to the F-theory Kähler sector on the Weak Gravity
Conjecture, which on the classical level is generically satisfied by the tower of excitations
of the emergent heterotic string. We argue that away from the strict weak coupling limit the
super-extremality bound of the Weak Gravity Conjecture is corrected by gauge threshold
and mass renormalisation effects. Duality between heterotic string theory and F-theory
can then be used to match the 0-corrections on the F-theory side to string loop corrections
on the heterotic side. Based on this and by imposing the Weak Gravity Conjecture to hold
also on the quantum level, we predict the form of the mass renormalisation of the tower of
string excitations.
Finally, we investigate the complex structure moduli space of such F-theory compactifications
in the presence of G4-flux. For an arbitrary dimension of this moduli space,
we present a systematic study of the flux potential and its vacua in the large complex
structure phase where each complex structure fields splits into a saxionic and an axionic
component. In particular we include polynomial corrections to the leading expressions of
Kähler and superpotential which, via four-fold mirror symmetry, can be identified with
curvature corrections in type IIA. For one family of flux choices, these corrections ensure
the stabilisation of all complex structure moduli without a parametric violation of the
tadpole cancellation at the cost of setting a bound on the possible saxionic vevs. In contrast,
for a second family of flux choices, the saxionic vevs can be unbounded with the
contribution to the D3-brane tadpole being independent of the dimension of the moduli
space

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**Google™ Scholar:**Wiesner, Max

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