相关论文: On $p$-integrality of instanton numbers
We give a simplified derivation of the expression of instanton numbers and of mirror map in terms of Frobenius map on p-adic cohomology and use this expression to prove integrality theorems. Modifying this proof we verify that the…
We study integrality of instanton numbers (genus zero Gopakumar - Vafa invariants) for quintic and other Calabi-Yau manifolds. We start with the analysis of the case when the moduli space of complex structures is one-dimensional; later we…
We prove the results announced in a joint paper (arXiv:hep-th/0603106) with Maxim Kontsevich and Albert Schwarz.
We apply mirror symmetry to the problem of counting holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines. As we found in Part A [hep-th/0703182], the integral homology group H_2(X,Z)=Z^3 + Z_3 + Z_3 contains…
We show that one can express Frobenius transformation on middle-dimensional p-adic cohomology of Calabi-Yau threefold in terms of mirror map and instanton numbers. We express the mirror map in terms of Frobenius transformation on p-adic…
We use mirror symmetry to determine and sum up a class of membrane instanton corrections to the hypermultiplet moduli space metric arising in Calabi-Yau threefold compactifications of type IIA strings. These corrections are mirror to the D1…
We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of…
We use instanton numbers to: (i) stratify moduli of vector bundles, (ii) calculate relative homology of moduli spaces and (iii) distinguish curve singularities.
Using Dwork's theory, we prove a broad generalisation of his famous p-adic formal congruences theorem. This enables us to prove certain p-adic congruences for the generalized hypergeometric series with rational parameters; in particular,…
The two applications are: 1. sometimes instanton numbers stratify moduli of bundles better than Chern numbers. 2. sometimes instanton numbers distinguish singularities better than the classical numerical invariants.
We present an algorithm for computing instanton numbers of curve singularities. A comparison is made between these and some other invariants of curve singularities. The algorithm has been implemented in the symbolic computer algebra program…
We review the deformed instanton equations making connection with Hilbert schemes and integrable systems. A single U(1) instanton is shown to be \asd\ with respect to the Burns metric.
We study, by means of mirror symmetry, the quantum geometry of the K\"ahler-class parameters of a number of Calabi-Yau manifolds that have $b_{11}=2$. Our main interest lies in the structure of the moduli space and in the loci corresponding…
We show that a number of multiple integrals may viewed as tau functions of various integrable hierarchies. The instanton contributions in the two-dimensional O(3)$\ \sigma $ model is an example of such an approach.
We address nonperturbative dynamics of the two-dimensional bosonic and supersymmetric $\mathbb{C}P^{N-1}$ models for general $N$ by developing new tools directly on $\mathbb{R}^2$. The analysis starts with a new formulation of instantons…
We prove some integrality properties of the open-closed mirror maps, inverse open-closed mirror maps and mirror curves of some local Calabi-Yau geometries.
We determine the instanton corrected hypermultiplet moduli space in type IIB compactifications near a Calabi-Yau conifold point where the size of a two-cycle shrinks to zero. We show that D1-instantons resolve the conifold singularity…
We compute the normalization of the general multi-instanton contribution to the partition function of $(p',p)$ minimal string theory and also to the dual two-matrix integral. We find perfect agreement between the two results.
We prove the `integrality of Taylor coefficients of mirror maps' conjecture for Greene--Plesser mirror pairs as a natural byproduct of an arithmetic refinement of homological mirror symmetry. We also prove homological mirror symmetry for…
This is the third article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. It is explained how to compute the instanton partition functions. The results can be written as sums over bases…