WZW - Poisson manifolds

By C. Klimčík, T. Strobl. 2001

157 citations recorded by the source corpus.

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting “WZW–Poisson” manifold M is characterized by a bivector Π and by a closed three-form H such that 1/2[Π,Π]Schouten=〈H,Π⊗Π⊗Π〉.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7a76588bd4b72ae1e002c97bb45b0ebcb8b6dafd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Integration of twisted Dirac brackets (2003, background): “Connections between Poisson geometry and topological sigma models (see [20], [26]) have led to the notion of Poisson structures twisted by a closed 3-form, which were described by Severa and Weinstein in [27] as special cases of twisted Dirac structures.”
Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory (2003, methodology): “son structures) The WZW-Poisson structures introduced by Klimčik and Strobl [25] were studied by Ševera and Weinstein in 2001 [48], who called them Poisson structures with background, and also twisted Poisson structures.”
Quasi-Lie Bialgebroids and Twisted Poisson Manifolds (2001, methodology): “The latter appeared recently in works of Park [14], Cornalba-Schiappa [2] and Klimčik-Strobl [5] on string theory, and were studied by Ševera and Weinstein [17] using Courant algebroids and Dirac structures.”
Non‐geometric fluxes in supergravity and double field theory (2012, background): “in [100–102]; the magnetic B-field of the monopole corresponds to the bi-vector β in our case, and the non-closure of B corresponds to the R flux.”
Derived Brackets (2003, background): “, a WZW-Poisson structure in the sense of Klimčik and Strobl [23].”
Generalized Complex Manifolds and Supersymmetry (2004, background): “In the case G = 0 and d(B − b) 6= 0 the model can be related to more general type of topological theory, the WZ-Poisson sigma model [23], assuming some specific differential condition between θ and d(B − b).”
Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, methodology): “which is the action of the H-twisted Poisson sigma-model with target space M [68, 57].”