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A Path Integral Approach¶to the Kontsevich Quantization Formula
Abstract: 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 pathExpand
The geometry of WZW branes
The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and byExpand
BRST approach to minimal models
We introduce a BRST charge in a series of Coulomb gas models in two dimensions. We show that these models, once restricted to BRST states, are equivalent to the minimal two-dimensional conformalExpand
Elliptic quantum groups
  • G. Felder
  • Mathematics, Physics
  • 22 December 1994
This note for the Proceedings of the International Congress of Mathematical Physics gives an account of a construction of an ``elliptic quantum group'' associated with each simple classical LieExpand
Conformal Field Theory and Integrable Systems Associated to Elliptic Curves
It has become clear over the years that quantum groups (i.e., quasitriangular Hopf algebras, see [D]) and their semiclassical counterpart, Poisson Lie groups, are an essential algebraic structureExpand
Fock representations and BRST cohomology inSL(2) current algebra
We investigate the structure of the Fock modules overA1(1) introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex ofExpand
Poisson sigma models and symplectic groupoids
We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in theExpand
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 onExpand
Relative formality theorem and quantisation of coisotropic submanifolds
We prove a relative version of Kontsevich's formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich's theorem if C=M. It states that the DGLA ofExpand
Spectra of Wess-Zumino-Witten models with arbitrary simple groups
We consider the Wess-Zumino-Witten two-dimensional sigma models with fields taking values in an arbitrary connected (but not necessarily simply connected) simple Lie groupG. The quantum states of theExpand