Related papers: Doubled Formalism, Complexification and Topologica…
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 two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In…
The AKSZ construction was developed as a geometrical formalism to find the solution to the classical master equation in the BV quantization of topological branes based on the concept of QP manifolds. However, the formalism does not apply in…
Consistent boundary conditions for Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma models and the corresponding boundary theories are analyzed. As their mathematical structures, we introduce a generalization of differential graded…
We give a self-contained survey of some approaches aimed at a global description of the geometry underlying double field theory. After reviewing the geometry of Courant algebroids and their incarnations in the AKSZ construction, we develop…
This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky…
We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a…
In this paper we describe multigraded generalizations of some constructions useful for mathematical understanding of gauge theories: we perform a near-at-hand generalization of the Aleksandrov--Kontsevich--Schwarz--Zaboronsky procedure, we…
We study the topological sector of N=2 sigma-models with H-flux. It has been known for a long time that the target-space geometry of these theories is not Kahler and can be described in terms of a pair of complex structures, which do not…
The Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) construction encodes all the data of a topological sigma-model in the finite-dimensional symplectic $Q$-manifold. Relaxing the nondegeneracy condition i.e. considering a presymplectic form…
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to the a generalization of the Weil model worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field theory,…
We generalize the AKSZ construction of topological field theories to allow the target manifolds to have possibly-degenerate (homotopy) Poisson structures. Classical AKSZ theories, which exist for all oriented spacetimes, are described in…
We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. Generically these are topological membrane models, and we show that…
Using the AKSZ prescription we construct 2D and 3D topological field theories associated to generalized complex manifolds. These models can be thought of as 2D and 3D generalizations of A- and B-models. Within the BV framework we show that…
By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson…
We review and extend the Alexandrov-Kontsevich-Schwarz-Zaboronsky construction of solutions of the Batalin-Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a…
We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4,…
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is $A$ model in the case that the generalized complex structuredepends on only a symplectic structure. Our…
We extend the AKSZ formulation of the Poisson sigma model to more general target spaces, and we develop the general theory of graded geometry for poly-symplectic and poly-Poisson structures. In particular we prove a Schwarz-type theorem and…