اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدComputation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture
483
0
0.0
(
0
)
تأليف
Bertrand Eynard
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The BKMP conjecture (2006-2008), proposed a new method to compute closed and open Gromov-Witten invariants for every toric Calabi-Yau 3-folds, through a topological recursion based on mirror symmetry. So far, this conjecture had been verified to low genus for several toric CY3folds, and proved to all genus only for C^3. In this article we prove the general case. Our proof is based on the fact that both sides of the conjecture can be naturally written in terms of combinatorial sums of weighted graphs: on the A-model side this is the localization formula, and on the B-model side the graphs encode the recursive algorithm of the topological recursion. One can slightly reorganize the set of graphs obtained in the B-side, so that it coincides with the one obtained by localization in the A-model.Then it suffices to compare the weights of vertices and edges of graphs on each side, which is done in 2 steps: the weights coincide in the large radius limit, due to the fact that the toric graph is the tropical limit of the mirror curve. Then the derivatives with respect to Kahler radius coincide due to special geometry property implied by the topological recursion.
قيم البحث
اقرأ أيضاً
We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence we establish a wall-crossing formula for the generating functi
on of the counting invariants of perverse coherent systems. As an application we provide certain equations on Donaldson-Thomas, Pandeharipande-Thomas and Szendrois invariants. Finally, we show that moduli spaces associated with a quiver given by successive mutations are realized as the moduli spaces associated the original quiver by changing the stability conditions.
We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm, Marino, and Va
fa of the Gromov-Witten theory of local Calabi-Yau toric 3-folds are proven to be correct in the full 3-leg setting.
We construct a global B-model for weighted homogeneous polynomials based on K. Saitos theory of primitive forms. Our main motivation is to give a rigorous statement of the so called global mirror symmetry conjecture relating Gromov-Witten invariants
and Fan--Jarvis--Ruan--Witten invariants. Furthermore, our construction allows us to generalize the notion of a quasi-modular form and holomorphic anomaly equations. Finally, we prove the global mirror symmetry conjecture for the Fermat polynomials.
We construct Lagrangian sections of a Lagrangian torus fibration on a 3-dimensional conic bundle, which are SYZ dual to holomorphic line bundles over the mirror toric Calabi-Yau 3-fold. We then demonstrate a ring isomorphism between the wrapped Floer
cohomology of the zero-section and the regular functions on the mirror toric Calabi-Yau 3-fold. Furthermore, we show that in the case when the Calabi-Yau 3-fold is affine space, the zero section generates the wrapped Fukaya category of the mirror conic bundle. This allows us to complete the proof of one direction of homological mirror symmetry for toric Calabi-Yau orbifold quotients of the form $mathbb{C}^3/Check{G}$. We finish by describing some elementary applications of our computations to symplectic topology.
We study Hilbert schemes of points on a smooth projective Calabi-Yau 4-fold $X$. We define $mathrm{DT}_4$ invariants by integrating the Euler class of a tautological vector bundle $L^{[n]}$ against the virtual class. We conjecture a formula for their
generating series, which we prove in certain cases when $L$ corresponds to a smooth divisor on $X$. A parallel equivariant conjecture for toric Calabi-Yau 4-folds is proposed. This conjecture is proved for smooth toric divisors and verified for more general toric divisors in many examples. Combining the equivariant conjecture with a vertex calculation, we find explicit positive rational weights, which can be assigned to solid partitions. The weighted generating function of solid partitions is given by $exp(M(q)-1)$, where $M(q)$ denotes the MacMahon function.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
