# Vector fields on mapping spaces and a converse to the AKSZ construction

@article{Voronov2012VectorFO, title={Vector fields on mapping spaces and a converse to the AKSZ construction}, author={Theodore Th. Voronov}, journal={arXiv: Mathematical Physics}, year={2012} }

The well-known AKSZ construction (for Alexandrov--Kontsevich--Schwarz--Zaboronsky) gives an odd symplectic structure on a space of maps together with a functional $S$ that is automatically a solution for the classical master equation $(S,S)=0$. The input data required for the AKSZ construction consist of a volume element on the source space and a symplectic structure of suitable parity on the target space, both invariant under given homological vector fields on the source and target. In this…

## 5 Citations

Lectures on AKSZ Topological Field Theories for Physicists

- Mathematics, Physics
- 2012

This lecture provides an introductory review about topological field theories (TFT) called AKSZ type. The AKSZ construction is mathematical formulation to unify a large class of TFTs, inspired by the…

Graded Geometry, Q‐Manifolds, and Microformal Geometry

- MathematicsFortschritte der Physik
- 2019

We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero. They can be seen as a…

On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms

- Mathematics
- 2020

Brane current algebras and generalised geometry from QP manifolds. Or, “when they go high, we go low”

- MathematicsJournal of High Energy Physics
- 2021

Abstract
We construct a Poisson algebra of brane currents from a QP-manifold, and show their Poisson brackets take a universal geometric form. This generalises a result of Alekseev and Strobl on…

Lectures on AKSZ Sigma Models for Physicists

- Mathematics
- 2017

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…

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