Fibration ≈ Fibration
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N = 3 $$ \mathcal{N}=3 $$ four dimensional field theories Open
We introduce a class of four dimensional field theories constructed by quotienting ordinary N=4 U(N ) SYM by particular combinations of R-symmetry and SL(2, ℤ) automorphisms. These theories appear naturally on the worldvolume of D3 branes …
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Seifert fibering operators in 3d $$ \mathcal{N}=2 $$ theories Open
A bstract We study 3d $$ \mathcal{N}=2 $$ supersymmetric gauge theories on closed oriented Seifert manifolds — circle bundles over an orbifold Riemann surface —, with a gauge group G given by a product of simply-connected and/or unitar…
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The Vietoris–Rips complexes of acircle Open
Given a metric space X and a distance threshold r>0, the Vietoris-Rips\nsimplicial complex has as its simplices the finite subsets of X of diameter\nless than r. A theorem of Jean-Claude Hausmann states that if X is a Riemannian\nmanifold …
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On the algebraic<i>K</i>-theory of higher categories Open
We prove that Waldhausen $K$-theory, when extended to a very general class of quasicategories, can be described as a Goodwillie differential. In particular, $K$-theory spaces admit canonical (connective) deloopings, and the $K$-theory func…
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Phases of 5d SCFTs from M-/F-theory on non-flat fibrations Open
We initiate the systematic investigation of non-flat resolutions of non-minimal singularities in elliptically fibered Calabi-Yau threefolds. Compactification of M-theory on these geometries provides an alternative approach to studying phas…
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F-theory Open
F-theory is probably 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 str…
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The F-theory geometry with most flux vacua Open
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold Mmax gives rise to O(10272,000) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all …
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On discrete symmetries and torsion homology in F-theory Open
We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a $$ {\mathbb{Z}}_2 $$ symmetry, we show that there are t…
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Scalar optical hopfions Open
Hopfions are three-dimensional (3D) topological states discovered in field theory, magnetics, and hydrodynamics that resemble particle-like objects in physical space. Hopfions inherit the topological features of the Hopf fibration, a homot…
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6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces Open
We carry out a systematic study of a class of 6D F-theory models and associated Calabi-Yau threefolds that are constructed using base surfaces with a generalization of toric structure. In particular, we determine all smooth surfaces with a…
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A new construction of Calabi–Yau manifolds: Generalized CICYs Open
We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi-Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility st…
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Swampland bounds on the Abelian gauge sector Open
We derive bounds on the number of Abelian gauge group factors in six-dimensional gravitational theories with minimal supersymmetry and in their F-theoretic realizations. These bounds follow by requiring consistency of certain Bogomol’nyi-P…
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On the fibration method for zero-cycles and rational points Open
Conjectures on the existence of zero-cycles on arbitrary smooth projective\nvarieties over number fields were proposed by Colliot-Th\\'el\\`ene, Sansuc, Kato\nand Saito in the 1980's. We prove that these conjectures are compatible with\nfi…
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A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold Open
Let $X$ be a general cubic $4$-fold. It was observed by Donagi and Markman that the relative intermediate Jacobian fibration $\\mathcal{J}_U/U$ (with $U=(\\mathbb{P}^5)^\\vee\\setminus X^\\vee$) associated with the family of smooth hyperpl…
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Fibration symmetries uncover the building blocks of biological networks Open
A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these n…
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Supersymmetric AdS3 supergravity backgrounds and holography Open
We analyse the conditions for AdS3 × ℳ7 backgrounds with pure NS-NS flux to be supersymmetric. We classify all N=(2, 2) solutions where ℳ7 satisfies the stronger condition of being a U(1)-fibration over a Kähler manifold. We compute the BP…
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TASI Lectures on F-theory Open
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 stri…
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Legendrian fronts for affine varieties Open
In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First, we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian hand…
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Box graphs and resolutions I Open
Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework tha…
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Rectification of enriched ∞-categories Open
We prove a rectification theorem for enriched ∞-categories: If V is a nice monoidal model category, we show that the homotopy theory of ∞-categories enriched in V is equivalent to the familiar homotopy theory of categories strictly enriche…
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Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations Open
We realize higher-form symmetries in F-theory compactifications on non-compact elliptically fibered Calabi-Yau manifolds. Central to this endeavour is the topology of the boundary of the non-compact elliptic fibration, as well as the expli…
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Induced automorphisms on irreducible symplectic manifolds: Open
We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of K3[n]-type is, in fact, induced by an automorphism of a K3 surface, and the manifold is a moduli spac…
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Origin of Abelian gauge symmetries in heterotic/F-theory duality Open
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the …
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Systematics of the α′ expansion in F-theory Open
Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative stri…
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Loop-by-loop differential equations for dual (elliptic) Feynman integrals Open
A bstract We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual for…
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Combinatorics and topology of proper toric maps Open
We study the topology of toric maps. We show that if f : X → Y {f\colon X\to Y} is a proper toric morphism, with X simplicial, then the cohomology of every fiber of f is pure and of Hodge–Tate type. When the map is a fibration, we gi…
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ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS Open
We use Toeplitz operators to evaluate the leading term in the asymptotics of the analytic torsion forms associated with a family of flat vector bundles $F_{p}$ . For $p\in \mathbf{N}$ , the flat vector bundle $F_{p}$ is the direct image of…
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Homotopy limits in type theory Open
Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the challenges posed by this approach to the formalizing homotopy-theoreti…
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On the homotopy groups of spheres in homotopy type theory Open
The goal of this thesis is to prove that $π_4(S^3) \simeq \mathbb{Z}/2\mathbb{Z}$ in homotopy type theory. In particular it is a constructive and purely homotopy-theoretic proof. We first recall the basic concepts of homotopy type theory, …
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Type IIB flux vacua from G-theory II Open
We find analytic solutions of type IIB supergravity on geometries that\nlocally take the form $\\text{Mink}\\times M_4\\times \\mathbb{C}$ with $M_4$ a\ngeneralised complex manifold. The solutions involve the metric, the dilaton,\nNSNS and…