Related papers: Dimer models and Calabi-Yau algebras

In their paper Livn\'e and Yui (math.AG/0304497) discuss several examples of non-rigid Calabi-Yau varieties which admit semi-stable K3-fibrations with 6 singular fibres over a base which is a rational modular curve. They also establish the…

We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following…

While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in…

We study some aspects of the recently discovered connection between dimer models and D-brane gauge theories. We argue that dimer models are also naturally related to closed string theories on non compact orbifolds of $\BC^2$ and $\BC^3$,…

In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of…

Motivated by S-duality modularity conjectures in string theory, we define new invariants counting a restricted class of 2-dimensional torsion sheaves, enumerating pairs $Z\subset H$ in a Calabi-Yau threefold X. Here H is a member of a…

The theory of coverings of the two-dimensional torus is a standard part of algebraic topology and has applications in several topics in string theory, for example, in topological strings. This paper initiates applications of this theory to…

Let $G \leq \operatorname{SL}_{n+1}(\mathbb{C})$ act on $R = \mathbb{C}[X_1, \ldots, X_{n+1}]$ by change of variables. Then, the skew-group algebra $R \ast G$ is bimodule $(n+1)$-Calabi-Yau. Under certain circumstances, the algebra admits a…

Let $X$ be a compact K\"ahler manifold and $\alpha$ a K\"ahler class on $X$. We prove that if $(X,\alpha)$ is uniformly K-stable for models, then there is a unique cscK metric in $\alpha$. This was first proved in the algebraic case by Chi…

Let $\mathcal{A}$ be a connected cochain DG algebra, whose underlying graded algebra $\mathcal{A}^{\#}$ is the quantum affine $n$-space $\mathcal{O}_{-1}(k^n)$. We compute all possible differential structures of $\mathcal{A}$ and show that…

The aim of this paper is to study bimodule stably Calabi-Yau properties of derivation quotient algebras. We give the definition of a twisted stably Calabi-Yau algebra and show that every twisted derivation quotient algebra $A$ for which the…

We show that when two toric Calabi-Yau 3-folds and their corresponding toric varieties are related by a birational transformation, they are associated with a pair of dimer models on the 2-torus that define dimer integrable systems, which…

In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…

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…

Tests of duality between heterotic strings on $K3\times T^2$ (restricted on certain Narain moduli subspaces) and type IIA strings on K3-fibered Calabi-Yau threefolds are attempted in the weak coupling regime on the heterotic side by…

Twisted Calabi-Yau algebras are a generalisation of Ginzburg's notion of Calabi-Yau algebras. Such algebras A come equipped with a modular automorphism \sigma \in Aut(A), the case \sigma = id being precisely the original class of Calabi-Yau…

We introduce new techniques based on brane tilings to investigate D3-branes probing orientifolds of toric Calabi-Yau singularities. With these new tools, one can write down many orientifold models and derive the resulting low-energy gauge…

We show that questions concerning the topological B-model on a Calabi-Yau manifold in the Landau-Ginzburg phase can be rephrased in the language of commutative algebra. This yields interesting and very practical methods for analyzing the…

Recently, string theory on Calabi--Yau manifolds was constructed and was shown to be a fully consistent, space--time supersymmetric string theory. The physically interesting case is the case of three generations. Intriguingly, it appears at…

We first review aspects of Kac Moody indefinite algebras with particular focus on their hyperbolic subset. Then we present two field theoretical systems where these structures appear as symmetries. The first deals with complete…