On the AKSZ formulation of the Poisson sigma model

Abstract

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 special case of this construction yields the Batalin-Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds.

19 pages

References in corpus (4)

• Deformation quantization of Poisson manifolds, I
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Topological Open P-Branes
• Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops

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