Related papers: Gopakumar-Vafa invariants and wall-crossing

We briefly review the formal picture in which a Calabi-Yau $n$-fold is the complex analogue of an oriented real $n$-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a…

Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is called the BCOV invariant. In this paper, we extend the BCOV invariant to such pairs $(X,D)$, where $X$ is a compact K\"ahler…

We investigate the Gopakumar-Vafa (GV) theory of local curves, namely, the total spaces of rank two vector bundles with canonical determinant on smooth projective curves. Under a certain genericity condition on the rank two bundles, we…

We study the asymptotic form of the Gopakumar-Vafa invariants at all genera for Calabi-Yau toric threefolds which have the structure of fibration of the A_n singularity over P^1. We claim that the asymptotic form is the inverse Laplace…

Let Y be a Calabi-Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the twisted I-function is one-dimensional, and spanned by the Gram matrix…

We propose a new exact quantization condition for a class of quantum mechanical systems derived from local toric Calabi-Yau three-folds. Our proposal includes all contributions to the energy spectrum which are non-perturbative in the Planck…

We prove a conjectural vanishing result for Gopakumar--Vafa invariants of quintic 3-folds, referred to as Castelnuovo bound in the literature. Furthermore, we calculate Gopakumar--Vafa invariants at Castelnuovo bound…

We prove Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds. It's also proved that the local Gopakumar-Vafa invariants of a given class at large genus vanish.

In this paper, we investigate the space of certain weak stability conditions on the triangulated category of D0-D2-D6 bound states on a smooth projective Calabi-Yau 3-fold. In the case of a quintic 3-fold, the resulting space is interpreted…

In arXiv:1008.1018 it is shown that a given stable vector bundle $V$ on a Calabi-Yau threefold $X$ which satisfies $c_2(X)=c_2(V)$ can be deformed to a solution of the Strominger system and the equations of motion of heterotic string…

We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of…

Donaldson-Thomas theory on a Calabi-Yau can be described in terms of a certain six-dimensional cohomological gauge theory. We introduce a certain class of defects in this gauge theory which generalize surface defects in four dimensions.…

The Gopakumar-Vafa conjecture predicts that the BPS invariants of a symplectic 6-manifold, defined in terms of the Gromov-Witten invariants, are integers and all but finitely many vanish in every homology class. The integrality part of this…

We apply results on inducing stability conditions to local Calabi-Yau threefolds and obtain applications to Donaldson-Thomas (DT) theory. A basic example is the total space of the canonical bundle of $Z=\mathbb{P}^1\times \mathbb{P}^1$. We…

Let $\sigma$ be a stability condition on the bounded derived category $D^b({\mathop{\rm Coh}\nolimits} W)$ of a Calabi-Yau threefold $W$ and $\mathcal{M}$ a moduli stack parametrizing $\sigma$-semistable objects of fixed topological type.…

We prove transformation formulae for generating functions of Gromov-Witten invariants on general toric Calabi-Yau threefolds under flops. Our proof is based on a combinatorial identity on the topological vertex and analysis of fans of toric…

The multi-Banana configuration $\widehat{F}_{mb}$ is a local Calabi-Yau threefold of Schoen type. Namely, $\widehat{F}_{mb}$ is a conifold resolution of $\widehat{I}_v \times_{\bf{D}} \widehat{I}_w$, where $\widehat{I}_v \to {\bf{D}}$ is an…

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of…

Recently, Cao-Maulik-Toda defined stable pair invariants of a compact Calabi-Yau 4-fold $X$. Their invariants are conjecturally related to the Gopakumar-Vafa type invariants of $X$ defined using Gromov-Witten theory by Klemm-Pandharipande.…

We prove a conjecture of Jockers-Mayr and Garoufalidis-Scheidegger, relating genus zero quantum $K$-invariants and Gopakumar--Vafa invariants on the quintic threefold.