A bstract We test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we analyze limit Kähler moduli space where coupling tends zero while is kept dynamical. show that such must be located at infinite distance space. As expected, low-energy effective breaks down this due tower charged particles becoming massless. These are excitations an asymptotically tensionless string, which...

A bstract As a refinement of the Swampland Distance Conjecture, we propose that quantum gravitational theory in an infinite distance limit its moduli space either decompactifies, or reduces to asymptotically tensionless, weakly coupled string theory. We support our claim by classifying, as special cases, behaviour M-Theory and Type IIA compactifications on Calabi-Yau three-folds at distances Kähler space. The analysis comprises three parts: first classify possible limits classical...

A bstract We systematically analyse weak coupling limits for 2-form tensor fields in the presence of gravity. Such are significant testing various versions Weak Gravity and Swampland Distance Conjectures, more broadly, phenomenon emergence. The 2-forms correspond to certain infinite-distance moduli space string compactifications, where asymptotically tensionless, solitonic strings arise. These identified as weakly coupled fundamental a dual frame, which makes idea emergence manifest....

We review recent progress in determining the effects of D-brane instantons N=1 supersymmetric compactifications Type II string theory to four dimensions. describe abstract instanton calculus for holomorphic couplings such as superpotential, gauge kinetic function and higher fermionic F-terms. This includes a discussion multi-instanton implications background fluxes sector. Our presentation also highlights, but is not restricted computation quiver theories on D-branes at singularities. then...

These lecture notes are devoted to formal and phenomenological aspects of F-theory. We begin with a pedagogical introduction the general concepts F-theory, covering classic topics such as connection Type IIB orientifolds, geometry elliptic fibrations emergence gauge groups, matter Yukawa couplings. As suitable framework for construction compact F-theory vacua we describe special class Weierstrass models called Tate models, whose local properties captured by spectral cover construction. Armed...

The existence of abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry internal Calabi-Yau fourfold and has important phenomenological consequences. We study conceptual aspects such U(1) along Coulomb Higgs branch. As one application we examine factors arising after a certain restriction Tate model that goes beyond local spectral cover analysis. In SU(5) GUT models this mechanism enforces U(1)_X symmetry prevents dimension-4 proton decay...

We prove a version of the Weak Gravity Conjecture for 6d F-theory or heterotic string compactifications with 8 supercharges. This sharpens our previous analysis by including massless scalar fields. The latter are known to modify bound in two priori independent ways: First, extremality condition charged black hole is modified, and second, test particles required satisfy subject additional Yukawa type interactions. argue on general grounds that at weak coupling, types effects equivalent tower...

We present a systematic construction of F-theory compactifications with Abelian gauge symmetries in addition to non-Abelian group G. The formalism is generally applicable models global Tate form but we focus on the phenomenologically interesting case G=SU(5). factors arise due extra sections resulting from specific factorisation polynomial which describes elliptic fibration. These constructions, accommodate up four different U(1) factors, are worked out detail for two possible embeddings...

We study the global structure of gauge group G F-theory compactified on an elliptic fibration Y. The properties are encoded in torsion subgroup Mordell-Weil rational sections Generalising Shioda map to torsional we construct a specific integer divisor class Y as fractional linear combination resolution divisors associated with Cartan subalgebra G. This can be interpreted element refined coweight lattice group. As result, spectrum admissible matter representations is strongly constrained and...

We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory compactifications with N = 1 supersymmetry. Extending our previous work on nearly tensionless heterotic strings in six dimensions, we show that under certain assumptions a tower of asymptotically massless states arises limit vanishing coupling U(1) gauge symmetry coupled to gravity. This contains super-extremal whose charge-to-mass ratios are larger than those extremal dilatonic Reissner-Nordström black holes,...

A bstract We study quantum corrections in four-dimensional theories with N = 1 supersymmetry the context of Quantum Gravity Conjectures. According to Emergent String Conjecture, infinite distance limits gravity either lead decompactification theory or result a weakly coupled string theory. verify this conjecture framework supersymmetric F-theory compactifications four dimensions including perturbative α′ as well non-perturbative corrections. After proving uniqueness emergent critical at...

A bstract We interpret infinite-distance limits in the complex structure moduli space of F-theory compactifications to six dimensions light general ideas quantum gravity. The we focus on arise from non-minimal singularities elliptic fiber over curves a Hirzebruch surface base, which do not admit crepant resolution. Such degenerations take place along infinite directions non-perturbative brane F-theory. blow-up procedure, detailed generally Part I this project [1], gives rise an internal...

Nonperturbative $D$-brane instantons can generate perturbatively absent though phenomenologically relevant couplings for type II orientifold compactifications with $D$-branes. We discuss the generation of vanishing $SU(5)$ GUT Yukawa coupling $⟨\mathbf{10}\text{ }\mathbf{10}\text{ }{\mathbf{5}}_{H}⟩$. Moreover, a simple globally consistent intersecting $D6$-brane model, we mass terms matter fields. This serve as mechanism decoupling exotic matter.

We perform a detailed conformal field theory analysis of $D2$-brane instanton effects in four-dimensional type IIA string vacua with intersecting $D6$-branes. In particular, we explicitly compute induced fermion two-point couplings which play the role perturbatively forbidden Majorana mass terms for right-handed neutrinos or MSSM $\ensuremath{\mu}$ terms. These results can readily be extended to higher-dimensional operators. concrete realizations such nonperturbative effects, Euclidean has...

F-theory compactified on a Calabi-Yau fourfold naturally describes non- Abelian gauge symmetries through the singularity structure of elliptic fibration. In contrast are more difficult to study because their inherently global nature. We argue that in general compactifications there massive symmetries, such as uplift part U(N) group D7-branes, arise from non-Kähler resolutions dual M-theory setup. The four-dimensional vacuum with vanishing expectation values for fields corresponds limit....

Elliptic Calabi-Yau fibrations with Mordell-Weil group of rank two are constructed. Such geometries the basis for F-theory compactifications Abelian gauge groups in addition to non-Abelian symmetry. We present elliptic fiber both as a ${\mathrm{Bl}}^{2}{\mathbb{P}}^{2}[3]$ fibration and birationally equivalent Weierstra\ss{} form. The spectrum charged singlets their Yukawa interactions worked out generality. This framework can be combined toric construction tops implement additional groups....