Related papers: Geometric transitions and integrable systems
In two-dimensional statistical models possessing a discretely holomorphic parafermion, we introduce a modified discrete Cauchy-Riemann equation on the boundary of the domain, and we show that the solution of this equation yields integrable…
In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail…
Compactifications of the physical superstring to two dimensions provide a general template for realizing 2D conformal field theories coupled to worldsheet gravity, i.e. non-critical string theories. Motivated by this observation, in this…
In this paper we construct a special geometry over the moduli space of type II string vacua with both NS and RR fluxes turning on. Depending on what fluxes are turning on we divide into three cases of moduli space of generalized structures.…
In two spatial dimensions, the transition between topological and trivial Chern insulators exemplifies a class of beyond-Landau critical phenomena. We show that the interaction-driven multicritical point of this transition falls into the…
We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the…
This is the second article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. The space of vacua of class $\cal S$ theories on $R^3 \times S^1$ can be identified as the moduli space of…
In the first part of this paper, we obtain mirror formulas for twisted genus 0 two-point Gromov-Witten (GW) invariants of projective spaces and for the genus 0 two-point GW-invariants of Fano and Calabi-Yau complete intersections. This…
We consider four-dimensional supersymmetric compactifications of the E8 x E8 heterotic string on Calabi-Yau manifolds endowed with vector bundles with structure group SU(N) x U(1) and five-branes. After evaluating the Green-Schwarz…
We construct new topological theories related to sigma models whose target space is a seven dimensional manifold of G_2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the…
We review the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces. This relation has made possible to give an exact solution of topological string theory on these spaces to all orders in…
We construct a new, two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect non-interacting modes of different systems. We apply the new solution and…
In the class of (0,2) heterotic compactifications which has been constructed in the framework of gauged linear sigma models the Calabi-Yau varieties X are realized as complete intersections of hypersurfaces in toric varieties IP and the…
Toroidal 3-orbifolds $(S^1)^6/G$, for $G$ a finite group, were some of the earliest examples of Calabi-Yau 3-orbifolds to be studied in string theory. While much mathematical progress towards the predictions of string theory has been made…
The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. In the first part of this thesis, we study the action of mirror symmetry on two-dimensional…
For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that…
We offer a derivation of the duality between the topological U(1) gauge theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold. This duality was conjectured recently by Iqbal, Nekrasov, Okounkov, and Vafa. We deduce…
On promoting the type IIA side of the N=1 Heterotic/type IIA dual pairs of [1] to M-theory on a `barely G_2 Manifold' of [2], by spectrum-matching we show a possible triality between Heterotic on a self-mirror Calabi-Yau, M-theory on the…
For a one-parameter family of Calabi-Yau d-fold M embedded in ${{CP}^{d+1}}$, we consider a new quasi-topological field theory ${A^{\ast}}$(M)-model compared with the $A$(M)-model. The two point correlators on the sigma model moduli space…
$A_\infty$ categories are a mathematical structure that appears in topological field theory, string topology, and symplectic topology. This paper studies the cyclic homology of a Calabi-Yau $A_\infty$ category, and shows that it is…