2016/07/04 by Cesar Arias, Arias, Cesar, Per Sundell +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Covariant transformation #Degree (music) #Differential form #FOS: Physical sciences #Hamiltonian (control theory) #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical physics #Mathematics #Nilpotent #Physics #Poisson distribution #Pure mathematics #Quantum mechanics #Sigma #Sigma model #Supermanifold #Supersymmetry #hep-th
paper · pdf · doi:10.48550/arxiv.1607.00727
39 pages
arxiv created 2016/07/04 · openalex publication_date 2016/07/04 · arxiv updated 2016/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The induced two-dimensional topological N=1 supersymmetric sigma model on a differential Poisson manifold M presented in arXiv:1503.05625 is shown to be a special case of the induced Poisson sigma model on the bi-graded supermanifold T[0,1]M. The bi-degree comprises the standard N-valued target space degree, corresponding to the form degree on the worldsheet, and an additional Z-valued fermion number, corresponding to the degree in the differential graded algebra of forms on M. The N=1 supersymmetry stems from the compatibility between the (extended) differential Poisson bracket and the de Rham differential on M. The latter is mapped to a nilpotent vector field Q of bi-degree (0,1) on T*[1,0](T[0,1]M), and the covariant Hamiltonian action is Q-exact. New extended supersymmetries arise as inner derivatives along special bosonic Killing vectors on M that induce Killing supervector fields of bi-degree (0,-1) on T*[1,0](T[0,1]M).