2D sigma models and differential Poisson algebras

Abstract

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to any worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

20 pages

References in corpus (5)

• Poisson sigma model on the sphere
• 4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory
• A Star Product for Differential Forms on Symplectic Manifolds
• On Singleton Composites in Non-compact WZW Models
• Semi-classical differential structures

Cited by in corpus (9)

• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• 4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory
• Fronsdal fields from gauge functions in Vasiliev's higher-spin gravity
• Action principles for higher and fractional spin gravities
• Frobenius-Chern-Simons gauge theory
• Higher spin fluctuations on spinless 4D BTZ black hole
• Integrable Hopf twists, marginal deformations and generalised geometry
• Differential Poisson Sigma Models with Extended Supersymmetry
• Supersymmetric Poisson and Poisson-supersymmetric sigma models