The BV action of 3D twisted R-Poisson sigma models
arXiv:2206.03683 · doi:10.1007/JHEP10(2022)002
Abstract
We determine the solution to the classical master equation for a 3D topological field theory with Wess-Zumino term and an underlying geometrical structure of a twisted R-Poisson manifold on its target space. The graded geometry of the target space departs from the usual QP structure encountered in the AKSZ construction of topological sigma models, the obstruction being attributed to the presence of the Wess-Zumino 4-form. Due to the inapplicability of the AKSZ construction in this case, we set up the traditional BV/BRST formalism for twisted R-Poisson sigma models in any dimension, which feature an open gauge algebra and constitute multiple stages reducible constrained Hamiltonian systems. An unusual feature of the theories is that it exhibits non-linear openness of the gauge algebra, in other words products of the equations of motion appear in it. Nevertheless, we find the BV action in presence of the 4-form twist in 3D, namely for a specific 4-form twisted (pre-)Courant sigma model. Moreover, we provide a complete set of explicit formulas for the off-shell nilpotent BV operator for untwisted R-Poisson sigma models in any dimension.
arXiv comment32 pages
References in corpus (28)
- Deformation quantization of Poisson manifolds, I
- Quantum Field Theory on Noncommutative Spaces
- The Geometry of the Master Equation and Topological Quantum Field Theory
- A path integral approach to the Kontsevich quantization formula
- Antibracket, Antifields and Gauge-Theory Quantization
- Two-Dimensional Gravity and Nonlinear Gauge Theory
- Poisson Structure Induced (Topological) Field Theories
- WZW-Poisson manifolds
- AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
- Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
- Chern-Simons Gauge Theory coupled with BF Theory
- Double Field Theory and Membrane Sigma-Models
- Dirac Sigma Models
- BV Quantization of Topological Open Membranes
- Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
- Frame-like Lagrangians and presymplectic AKSZ-type sigma models
- Lie algebroids, gauge theories, and compatible geometrical structures
- A Deformation of Three Dimensional BF Theory
- Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory
- Gauging the Wess-Zumino term of a sigma model with boundary
- Sigma models for genuinely non-geometric backgrounds
- QP-Structures of Degree 3 and 4D Topological Field Theory
- Pre-Courant Algebroids
- Topological Field Theories induced by twisted R-Poisson structure in any dimension
- Gravity theory on Poisson manifold with -flux
- Courant sigma model and -algebras
- Topological Membranes, Current Algebras and H-flux - R-flux Duality based on Courant Algebroids
- Higher Affine Connections