When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion

We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. To this end we consider complex structure deformations of elliptic fibrations with a Mordell--Weil group of rank one and identify the conditions under which the generating section becomes torsional. For the specific case of Z2 torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU(2) x SU(4)]/Z2 x SU(2). The subsolution with gauge group SU(2)/Z2 x SU(2), for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Z2 torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU(2)/Z2 x Z2 gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations.Comment: 51 page

The local Callan-Symanzik equation: structure and applications

The local Callan-Symanzik equation describes the response of a quantum field theory to local scale transformations in the presence of background sources. The consistency conditions associated with this anomalous equation imply non-trivial relations among the $\beta$-function, the anomalous dimensions of composite operators and the short distance singularities of correlators. In this paper we discuss various aspects of the local Callan-Symanzik equation and present new results regarding the structure of its anomaly. We then use the equation to systematically write the n-point correlators involving the trace of the energy-momentum tensor. We use the latter result to give a fully detailed proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also correspond to CFTs. We also clarify the relation between the matrix entering the gradient flow formula for the $\beta$-function and a manifestly positive metric in coupling space associated with matrix elements of the trace of the energy momentum tensor.Comment: v2: Modified discussion of the amplitude; v3: typos fixe

Constraints on Four Dimensional Effective Field Theories From String and F-theory

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 E_8 to SU(5)x 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 compactications on a singular elliptic fibration via Matrix Factorisation, and find the charged spectrum of two non-Abelian examples

On E 8 and F-theory GUTs

Journal of High Energy Physics 2015.6 (2015): 039 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)We study correlations between the massless field spectra of F-theory fibrations supporting an SU(5) gauge symmetry extended by Abelian symmetries and the spectra that arise from the group E8. The adjoint representation of E8 leads to six different classes of matter spectra upon Higgsing E8 to SU(5)×U(1)n. Of 27 different smooth F-theory elliptic fibrations constructed in the literature, satisfying certain genericness and flatness criteria, the matter spectrum of only one can be embedded in these six theories, thereby apparently ruling out any connection. We define an extension of the spectrum arising from the adjoint of E8 by introducing new SU(5)-singlet fields with Abelian charges such that there exists a cubic gauge invariant coupling between any three representations. Higgsing by these new singlets leads to a further 20 classes of spectra, and we find that all the F-theory fibrations can then be embedded in this extended set. These results show that E8, when extended in this specific way, may still have a role to play in controlling the possible matter spectra in F-theory. We give an explicit geometric example of the presence of the extending singlets and their Higgsing. We discuss some phenomenological applications of the new set of theories, in particular due to the existence of a ℤ2 matter parity. Finally we make some comments on the Heterotic duals of the F-theory fibrations which extend E8 in this wayThe work of FB and EP is supported by the Heidelberg Graduate School for Fundamental Physic

Instanton corrections and emergent strings

We study limits of infinite distance in the moduli space of 4d N = 2 string compactifications, in which instanton effects dominate. We first consider trajectories in the hypermultiplet moduli space of type IIB Calabi-Yau compactifications. We observe a correspondence between towers of D-brane instantons and D-brane 4d strings, such that the lighter the string the more relevant the instanton effects are. The dominant instantons modify the classical trajectory such that the lightest D-brane string becomes tensionless even faster, while the other strings are prevented to go below the fundamental string tension. This lightest string is dual to a fundamental type IIB string and realises the Emergent String Conjecture. We also consider the vector multiplet moduli space of type I string theory on K3 ×T2, where quantum corrections can also become significant. Naively, we only find trajectories that correspond to decompactification limits, in apparent contradiction with the picture obtained in some dual setupThis work is supported by the Spanish Research Agency (Agencia Estatal de Investigación) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, and by the grant PGC2018-095976-B-C21 from MCIU/AEI/FEDER, UE. MW received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 713673. The work of MW also received the support of a fellowship from “la Caixa” Foundation (ID 100010434) with fellowship code LCF/BQ/DI18/1166003