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Related papers: $G_2$-manifolds from Diophantine equations

200 papers

We construct a new class of metastable de Sitter vacua of flux compactifications of type IIB string theory. These solutions provide a natural extension of the `Large Volume Scenario' anti-de Sitter vacua, and can analogously be realised at…

High Energy Physics - Theory · Physics 2017-10-31 Diego Gallego , M. C. David Marsh , Bert Vercnocke , Timm Wrase

Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus. We introduce the notion of f-twisted Sobolev spaces for the pair (X,f) and prove the corresponding Hodge-to-de Rham degeneration…

Mathematical Physics · Physics 2019-03-08 Si Li , Hao Wen

We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subspaces satisfying a highly generic and essentially optimal…

Number Theory · Mathematics 2026-02-12 Sam Chow , Rajula Srivastava , Niclas Technau , Han Yu

We consider N=1 F-theory and Type IIB orientifold compactifications and derive new \alpha' corrections to the four-dimensional effective action. They originate from higher derivative corrections to eleven-dimensional supergravity and…

High Energy Physics - Theory · Physics 2015-06-15 Thomas W. Grimm , Raffaele Savelli , Matthias Weissenbacher

F-theory compactified on a Calabi-Yau fourfold naturally describes non-Abelian gauge symmetries through the singularity structure of the elliptic fibration. In contrast Abelian symmetries are more difficult to study because of their…

High Energy Physics - Theory · Physics 2015-05-28 Thomas W. Grimm , Max Kerstan , Eran Palti , Timo Weigand

In the present paper, we reexamine the moduli stabilization problem of the Type IIB orientifolds with one complex structure modulus in a modified two-step procedure. The full superpotential including both the 3-form fluxes and the…

High Energy Physics - Theory · Physics 2008-11-26 Huan-Xiong Yang

We study perturbative compactifications of Type II string theory that rely on a fibration structure of the extra dimensions a la SYZ. Non-geometric spaces are obtained by using T-dualities as monodromies. These vacua generically preserve…

High Energy Physics - Theory · Physics 2009-03-04 David Vegh , John McGreevy

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics {\it also} stabilises the moduli in $M$ theory compactifications on manifolds of $G_2$-holonomy {\it without} fluxes. This gives stable vacua with…

High Energy Physics - Theory · Physics 2008-11-26 Bobby Acharya , Konstantin Bobkov , Gordon Kane , Piyush Kumar , Diana Vaman

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural…

Differential Geometry · Mathematics 2008-11-26 O. I. Mokhov

We study properties of flux vacua in type IIB string theory in several simple but illustrative models. We initiate the study of the relative frequencies of vacua with vanishing superpotential W=0 and with certain discrete symmetries. For…

High Energy Physics - Theory · Physics 2009-10-07 Oliver DeWolfe , Alexander Giryavets , Shamit Kachru , Washington Taylor

I review type IIB string compactifications in which the three-form field strengths satisfy a self-duality condition on the internal manifold. I begin with an overview of the models, giving preliminary formulae and several points of view…

High Energy Physics - Theory · Physics 2007-05-23 Andrew R. Frey

We study moduli stabilization of the F-theory compactified on an elliptically fibered Calabi-Yau fourfold. Our setup is based on the mirror symmetry framework including brane deformations. The complex structure moduli dependence of the…

High Energy Physics - Theory · Physics 2017-11-22 Yoshinori Honma , Hajime Otsuka

We consider heterotic target space dual (0,2) GLSMs on elliptically fibered Calabi-Yau manifolds. In this context, each half of the "dual" heterotic theories must in turn have an F-theory dual. Moreover, the apparent relationship between…

High Energy Physics - Theory · Physics 2019-12-18 Lara B. Anderson , He Feng , Xin Gao , Mohsen Karkheiran

We report on a new class of flux vacua generically present in Calabi-Yau compactifications of type-IIB string theory. At these vacua, the mass spectrum of the complete axio-dilaton/complex structure sector is given, to leading order in…

High Energy Physics - Theory · Physics 2021-05-12 Jose J. Blanco-Pillado , Kepa Sousa , Mikel A. Urkiola , Jeremy M. Wachter

In this note we construct large ensembles of supersymmetry breaking solutions arising in the context of flux compactifications of type IIB string theory. This class of solutions was previously proposed in arXiv:hep-th/0402135 for which we…

High Energy Physics - Theory · Physics 2023-08-31 Sven Krippendorf , Andreas Schachner

This work continues the study of $F$--manifolds $(M,\circ)$, first defined by Hertling and Manin and investigated in [He]. The notion of a compatible flat structure $\nabla$ is introduced, and it is shown that many constructions known for…

Differential Geometry · Mathematics 2007-05-23 Yuri I. Manin

Motivated by the question of whether scale-separated AdS$_3$ flux vacua arising from G$_2$ compactifications admit an uplift to eleven-dimensional supergravity, we construct scale-separated AdS$_3$ flux vacua in massless type IIA with only…

High Energy Physics - Theory · Physics 2026-03-30 George Tringas

In this paper, by using monotonicity formulas for vector bundle-valued $p$-forms satisfying the conservation law, we first obtain general $L^2$ global rigidity theorems for locally conformally flat (LCF) manifolds with constant scalar…

Differential Geometry · Mathematics 2016-04-19 Yuxin Dong , Hezi Lin , Shihshu Walter Wei

A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In…

High Energy Physics - Theory · Physics 2016-02-15 Pascal du Bosque , Falk Hassler , Dieter Lust

We prove a general result about the stability of geometric flows of "closed" sections of vector bundles on compact manifolds. Our theorem allows to prove a stability result for the modified Laplacian coflow in G2-geometry introduced by…

Differential Geometry · Mathematics 2020-02-03 Lucio Bedulli , Luigi Vezzoni