A bstract This paper presents a worldsheet theory describing holomorphic maps to twistor
space with\(\mathcal {N}\) fermionic directions. The theory is anomaly free when\(\mathcal …

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 analysis of a …

After a brief summary of the main properties of Poisson manifolds and Lie algebroids in
general, we survey recent work on the modular classes of Poisson and twisted Poisson …

Motivated from target space covariant formulations of topological sigma models and from a
graded-geometric approach to higher gauge theory, we study connections on Lie and …

A bstract Using methods of formal geometry, the Poisson sigma model on a closed surface is
studied in perturbation theory. The effective action, as a function on vacua, is shown to have …

Abstract top We shall give a survey of classical examples, together with algebraic methods
to deal with those structures: graded algebra, cohomologies, cohomology operations. The …

We study an equivariant extension of the Batalin–Vilkovisky formalism for quantizing gauge
theories. Namely, we introduce a general framework to encompass failures of the quantum …

Abstract Dedicated to Murray Gerstenhaber and Jim Stasheff Kontsevich's formality theorem
states that the differential graded Lie algebra of multidifferential operators on a manifold M is …

We describe a canonical reduction of AKSZ–BV theories to the cohomology of the source
manifold. We get a finite-dimensional BV theory that describes the contribution of the zero …

Generalized Calabi–Yau manifolds and the chiral de Rham complex Page 1 Advances in
Mathematics 223 (2010) 1815–1844 www.elsevier.com/locate/aim Generalized Calabi–Yau …