Topological Field Theories induced by twisted R-Poisson structure in any dimension

Abstract

We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions $\ge 2$ whose target space has a geometrical structure that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a field content comprising a set of scalar fields accompanied by gauge fields of degree $(1,p-1,p)$ we determine a generic Wess-Zumino topological field theory in $p+1$ dimensions with background data consisting of a Poisson 2-vector, a $(p+1)$-vector $R$ and a $(p+2)$-form $H$ satisfying a specific geometrical condition that defines a $H$-twisted $R$-Poisson structure of order $p+1$. For this class of theories we demonstrate how a target space covariant formulation can be found by means of an auxiliary connection without torsion. Furthermore, we study admissible deformations of the generic class in special spacetime dimensions and find that they exist in dimensions 2, 3 and 4. The two-dimensional deformed field theory includes the twisted Poisson sigma model, whereas in three dimensions we find a more general structure that we call bi-twisted $R$-Poisson. This extends the twisted $R$-Poisson structure of order 3 by a non-closed 3-form and gives rise to a topological field theory whose covariant formulation requires a connection with torsion and includes a twisted Poisson sigma model in three dimensions as a special case. The relation of the corresponding structures to differential graded Q-manifolds based on the degree shifted cotangent bundle $T^{\ast }[p]T^{\ast }[1]M$ is discussed, as well as the obstruction to them being QP-manifolds due to the Wess-Zumino term.

arXiv comment40 pages

References in corpus (35)

• Topological insulators and superconductors
• Topological Field Theory of Time-Reversal Invariant Insulators
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Mirror Manifolds And Topological Field Theory
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• Geometry of Batalin-Vilkovisky quantization
• WZW-Poisson manifolds
• Exotic Branes in String Theory
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Axion topological field theory of topological superconductors
• E_{11} origin of Brane charges and U-duality multiplets
• Chern-Simons Gauge Theory coupled with BF Theory
• Effective actions of non-geometric fivebranes
• Double Field Theory and Membrane Sigma-Models
• The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures
• D-Brane Wess-Zumino Terms and U-Duality
• General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroids
• BV Quantization of Topological Open Membranes
• Letters to Alan Weinstein about Courant algebroids
• Non-geometric String Backgrounds and Worldsheet Algebras
• On weak Lie 2-algebras
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry
• Nambu-Sigma model and effective membrane actions
• Gauging the Wess-Zumino term of a sigma model with boundary
• Sigma models for genuinely non-geometric backgrounds
• Noether's variational theorem II and the BV formalism
• QP-Structures of Degree 3 and 4D Topological Field Theory
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Courant sigma model and $L_{\infty }$-algebras
• Double field theory algebroid and curved $L_{\infty }$-algebras
• Duality and higher Buscher rules in p-form gauge theory and linearized gravity
• L-infinity bialgebroids and homotopy Poisson structures on supermanifolds

Cited by in corpus (8)

• The BV action of 3D twisted R-Poisson sigma models
• Topological Dirac Sigma Models and the Classical Master Equation
• Geometric BV for twisted Courant sigma models and the BRST power finesse
• Basic curvature and the Atiyah cocycle in gauge theory
• Generalized symmetries as homotopy Lie algebras
• Instances of Higher Geometry in Field Theory
• Supersymmetric Poisson and Poisson-supersymmetric sigma models
• Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds