Giovanni Felder

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We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin-Vilkovisky quantization yields a superconformal field theory. The associativity of the star product,(More)
This note gives an account of a construction of an “elliptic quantum group” associated with each simple classical Lie algebra. It is closely related to elliptic face models of statistical mechanics, and, in its semiclassical limit, to the Wess-Zumino-Witten model of conformal field theory on tori. More details are presented in [Fe] and complete proofs will(More)
General boundary conditions (“branes”) for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of(More)
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.(More)
We describe representation theory of the elliptic quantum group Eτ,η(sl2). It turns out that the representation theory is parallel to the representation theory of the Yangian Y (sl2) and the quantum loop group Uq(s̃l2). We introduce basic notions of representation theory of the elliptic quantum group Eτ,η(sl2) and construct three families of modules:(More)