The Poisson sigma model on closed surfaces

On the Aksz Formulation of the Poisson Sigma Model

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, t...

Generalized Complex Geometry and the Poisson Sigma Model

The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N = (2, 1) or N = (2, 2) supersymmetry, but a certain relation among the different Poisson structures is needed. Moreover, important relations of an additional almost complex structure are found, which have no ...

Graded Poisson - Sigma Models

The formalism of graded Poisson-sigma models allows the construction of N = (2, 2) dilaton supergravity in terms of a minimal number of fields. For the gauged chiral U(1) symmetry the full action, involving all fermionic contributions , is derived. The twisted chiral case follows by simple redefinition of fields. The equivalence of our approach to the standard second order one in terms of super...

Poisson Sigma Models on Surfaces with Boundary: Classical and Quantum Aspects

Vortices on closed surfaces

Key words: point vortices, Riemann surfaces, Green functions. We consider N point vortices s j of strengths κ j moving on a closed (compact, boundaryless, orientable) surface S with riemannian metric g. As far as we know, only the sphere or surfaces of revolution, the latter qualitatively, have been treated in the available literature. The aim of this note is to present an intrinsic geometric f...