Related papers: Discrete Wilson Lines in F-Theory
The orbits space of an irreducible linear representation of a finite group is a variety whose coordinate ring is the ring of invariant polynomials. Boris Dubrovin proved that the orbits space of the standard reflection representation of an…
In four-dimensional F-theory compactifications with N=1 supersymmetry the fields describing the dynamics of space-time filling 7-branes are part of the complex structure moduli space of the internal Calabi-Yau fourfold. We explicitly…
We study D-branes on smooth noncompact toric Calabi-Yau manifolds that are resolutions of abelian orbifold singularities. Such a space has a distinguished basis {S_i} for the compactly supported K-theory. Using local mirror symmetry we…
We prove a structure theorem for the Albanese maps of varieties with Q-linearly trivial log canonical divisors. Our start point is the action of a nonlinear algebraic group on a projective variety.
D3-branes are often a necessary ingredient in global compactifications of F-theory. In minimal realizations of flavor hierarchies in F-theory GUT models, suitable fluxes are turned on, which in turn attract D3-branes to the Yukawa points.…
We explore a large class of F-theory compactifications to four dimensions. We find evidence that gauge groups that cannot be Higgsed without breaking supersymmetry, often accompanied by associated matter fields, are a ubiquitous feature in…
We construct a general class of new time dependent solutions of non-linear sigma models coupled to gravity. These solutions describe configurations of expanding or contracting codimension two solitons which are not subject to a constraint…
A deep result of Voisin asserts that the Griffiths group of a general non-rigid Calabi-Yau (CY) 3-fold is infinitely generated. This theorem builds on an earlier method of hers which was implemented by Albano and Collino to prove the same…
Reflexive polygons have attracted great interest both in mathematics and in physics. This paper discusses a new aspect of the existing study in the context of quiver gauge theories. These theories are 4d supersymmetric worldvolume theories…
We extend the deformation theory algorithm of matrix factorizations to systems with more than one D-brane. The obstructions to the deformations are F-term equations which can be integrated to an effective superpotential. We demonstrate the…
We construct irreducible modules for twisted toroidal Lie algebras and extended affine Lie algebras. This is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules. We…
In the context of string dualities, fibration structures of Calabi-Yau manifolds play a prominent role. In particular, elliptic and K3 fibered Calabi-Yau fourfolds are important for dualities between string compactifications with four flat…
This is an outline of work in progress concerning an algebro-geometric form of the Strominger-Yau-Zaslow conjecture. We introduce a limited type of degeneration of Calabi-Yau manifolds, which we call toric degenerations. For these, the…
Discrete gauge groups naturally arise in F-theory compactifications on genus-one fibered Calabi-Yau manifolds. Such geometries appear in families that are parameterized by the Tate-Shafarevich group of the genus-one fibration. While the…
A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elliptically fibered Calabi-Yau manifold on which the heterotic…
We analyze exotic matter representations that arise on singular seven-brane configurations in F-theory. We develop a general framework for analyzing such representations, and work out explicit descriptions for models with matter in the…
We demonstrate how to find modular discrete symmetry groups for $Z_N$ orbifolds. The $Z_7$ orbifold is treated in detail as a non-trivial example of a $(2,2)$ orbifold model. We give the generators of the modular group for this case which,…
We study the effective physics of F-theory at order $\alpha'^3$ in derivative expansion. We show that the ten-dimensional type IIB eight-derivative couplings involving the graviton and the axio-dilaton naturally descend from pure gravity in…
In this paper, a procedure is developed to construct compact F-theory fourfolds corresponding to perturbative IIB O7/O3 models on CICY threefolds with permutation involutions. The method is explained in generality, and then applied to…
F-theory is perhaps the most general currently available approach to study non-perturbative string compactifications in their geometric, large radius regime. It opens up a wide and ever-growing range of applications and connections to…