Quantum geometry of elliptic Calabi-Yau manifolds
TLDR
In this paper, a holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base.Abstract:
We study the quantum geometry of the class of Calabi-Yau threefolds, which are elliptic brations over a two-dimensional toric base. A holomorphic anomaly equation for the topological string free energy is proposed, which is iterative in the genus expansion as well as in the curve classes in the base. T -duality on the bre implies that the topological string free energy also captures the BPSinvariants of D4-branes wrapping the elliptic bre and a class in the base. We verify this proposal by explicit computation of the BPS invariants of 3D4-branes on the rational elliptic surface.read more
Citations
More filters
Journal ArticleDOI
Tensionless Strings and the Weak Gravity Conjecture
TL;DR: In this paper, the authors test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory and show that such a limit must be located at infinite distance in the moduli space.
Journal ArticleDOI
M-Strings
TL;DR: In this paper, the elliptic genus of (4,4) N M-strings is constructed from a dual A_{n-1} quiver 6d gauge theory with U(1) gauge groups.
Journal ArticleDOI
Superconformal partition functions and non-perturbative topological strings
Guglielmo Lockhart,Cumrun Vafa +1 more
TL;DR: In this article, a non-perturbative definition for refined topological strings is proposed, which can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S5.
Journal ArticleDOI
A Stringy Test of the Scalar Weak Gravity Conjecture
TL;DR: In this paper, a version of the Weak Gravity Conjecture for 6d F-theory or heterotic string compactifications with 8 supercharges is presented, where the extremality condition of a charged black hole is modified and the test particles required to satisfy the weak gravity conjecture are subject to additional Yukawa type interactions.
Journal ArticleDOI
Refined stable pair invariants for E-, M- and [ p , q ]-strings
TL;DR: In this paper, the authors used mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on noncompact Calabi-Yau manifolds, based on del Pezzo surfaces and elliptic surfaces, in particular the half K3.
References
More filters
Book
The geometry of moduli spaces of sheaves
Daniel Huybrechts,Manfred Lehn +1 more
TL;DR: In this paper, the Grauert-Mullich Theorem is used to define a moduli space for sheaves on K-3 surfaces, and the restriction of sheaves to curves is discussed.
Journal ArticleDOI
Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
TL;DR: In this paper, the authors developed techniques to compute higher loop string amplitudes for twisted N = 2 theories with ε = 3 (i.e. the critical case) by exploiting the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured by a master anomaly equation.
Journal ArticleDOI
A Strong coupling test of S duality
Cumrun Vafa,Edward Witten +1 more
TL;DR: By studying the partition function of N = 4 topologically twisted supersymmetric Yang-Mills on four-manifolds, this paper made an exact strong coupling test of the Montonen-Olive strong-weak duality conjecture.
Journal Article
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.
Posted Content
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
Maxim Kontsevich,Yan Soibelman +1 more
TL;DR: In this article, the authors define new invariants of 3d Calabi-Yau categories endowed with a stability structure, which are elements of quantum tori over a version of the Grothendieck ring of varieties over the ground field.