Related papers: On a B-field transform of generalized complex stru…

In this article we discuss the geometry of moduli spaces of (1) flat bundles over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills bundles over complex submanifolds in Calabi-Yau manifolds. These moduli spaces reflect…

In this paper we introduce and study the ''convergent'' algebra (containing ''a'' and ''b'' and acting on holomorphic germs in ''a'') which naturally acts on the ''generalized Brieskorn modules'' associated to the Gauss-Manin connections of…

We revisit sigma models on target spaces given by a principal torus fibration $X\to M$, and show how treating the 2-form B as a gerbe connection captures the gauging obstructions and the global constraints on the T-duality. We show that a…

Let $X$ be a normal projective variety over an algebraically closed field of characteristic zero. Let $D$ be a reduced Weil divisor on $X$. Let $G$ be a reductive linear algebraic group. We introduce the notion of a logarithmic connection…

Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame…

We identify a deformation of the N=2 supersymmetric sigma model on a Calabi-Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X such deformations allow one to interpolate…

We construct a chain complex $\mathfrak{B}$ based on a double complex derived from the universal complex $X(\mathbb{Z}_2^n)$. It is shown that $\mathfrak{B}$ has a nontrivial homology only in degree $n-2$, which is isomorphic to the…

In a previous paper we have constructed a compactification $KGl_n$ of the general linear group $Gl_n$, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De…

Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable $\sigma$-models. They are constructed systematically…

Given a smooth toric variety X and an ample line bundle O(1), we construct a sequence of Lagrangian submanifolds of (C^*)^n with boundary on a level set of the Landau-Ginzburg mirror of X. The corresponding Floer homology groups form a…

We study AKSZ-type BV constructions for the topological A- and B-models within a double field theory formulation that incorporates backgrounds with geometric and non-geometric fluxes. We relate them to a Courant sigma-model, on an open…

A study of sigma models whose target space is a group G that admits a compatible Poisson structure is presented. The natural action of O(D,D;Z) on the generalised tangent bundle TG+T*G and a generalisation of the Courant bracket that…

We generalize Kontsevich's construction of L-infinity derivations of polyvector fields from the affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph…

Let $\mathcal X=[(\mathbb C^r\setminus Z)/G]$ be a toric Fano orbifold. We compute the Fourier transform of the $G$-equivariant quantum cohomology central charge of any $G$-equivariant line bundle on $\mathbb C^r$ with respect to certain…

We establish an isomorphism of complex $K$-theory of the moduli space $\check{\mathcal{M}}$ of $``SL_n"$-Higgs bundles of degree $d$ and rank $n$ (in the sense of Hausel--Thaddeus) and twisted complex $K$-theory of the orbifold…

We argue that for a certain class of symplectic manifolds the category of A-branes (which includes the Fukaya category as a full subcategory) is equivalent to a noncommutative deformation of the category of B-branes (which is equivalent to…

We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of $M$ by a metallic Riemannian structure $(J,g)$ on $M$, providing conditions for their…

In this work we uncover a connection that relates the 1-form and the 2-group symmetries of 5D SCFTs derived from geometric engineering methods to monodromies of the corresponding B-models via mirror symmetry. Viewing defects as branes…

Given a smooth projective toric variety X, we construct an A-infinity category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line…

We present in this paper a construction for Gabor-type frames built out of generalized Weyl-Heisenberg groups. These latter are obtained via central extensions of groups which are direct products of locally compact abelian groups and their…