Related papers: Peacock patterns and new integer invariants in top…
Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank $r\ge1$ on $X$ in…
We study string theory on orbifolds in the presence of an antisymmetric constant background field and discuss some of new aspects of the theory. It is shown that the term with the antisymmetric field has a topological nature like a…
A double scaling limit can be defined in string theory on a Calabi-Yau (CY) manifold by approaching a point in moduli space where the CY space develops an isolated singularity and at the same time taking the string coupling to zero, while…
Using the generalised AdS/CFT correspondence, we show that there are certain ten-dimensional differentiable manifolds such that string theory on such a manifold is unstable [to the emission of "large branes"] no matter what the metric may…
The Gopakumar-Vafa invariants are numbers defined as certain linear combinations of the Gromov-Witten invariants. We prove that the GV invariants of a toric Calabi-Yau threefold are integers and that the invariants for high genera vanish.…
The Stokes multipliers in the matrix models are invariants in the string-theory moduli space and related to the D-instanton chemical potentials. They not only represent non-perturbative information but also play an important role in…
This work addresses nonperturbative effects in both matrix models and topological strings, and their relation with the large-order behavior of the 1/N expansion. We study instanton configurations in generic one-cut matrix models, obtaining…
Non-perturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order $e^{-1/g_s}$ contributions, where $g_s$ is the string coupling. The…
We consider the geometric transition and compute the all-genus topological string amplitudes expressed in terms of Hopf link invariants and topological vertices of Chern-Simons gauge theory. We introduce an operator technique of…
Consider zero-dimensional Donaldson-Thomas invariants of a toric threefold or toric Calabi-Yau fourfold. In the second case, invariants can be defined using a tautological insertion. In both cases, the generating series can be expressed in…
In arXiv:2306.07329 we established a connection between symplectic cuts of Calabi-Yau threefolds and open topological strings, and used this to introduce an equivariant deformation of the disk potential of toric branes. In this paper we…
We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber)…
I will discuss recent progress by many people in the program of extending natural topological invariants from manifolds to singular spaces. Intersection homology theory and mixed Hodge theory are model examples of such invariants. The past…
We point out that the celebrated Hawking effect of quantum instability of black holes seems to be related to a nonperturbative effect in string theory. Studying quantum dynamics of strings in the gravitational background of black holes we…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
We show that Calabi-Yau crystals generate certain Chern-Simons knot invariants, with Lagrangian brane insertions generating the unknot and Hopf link invariants. Further, we make the connection of the crystal brane amplitudes to the…
An elementary introduction to knot theory and its link to quantum field theory is presented with an intention to provide details of some basic calculations in the subject, which are not easily found in texts. Study of Chern-Simons theory…
We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR fluxes. The…
In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing…
Open topological string partition function gives rise to open Gromov-Witten invariants, open Donaldson-Thomas invariants and 3D-5D BPS indices. Utilizing the remodelling conjecture which connects topological recursion and topological string…