Brane wrapping, AKSZ sigma models, and QP manifolds

2023/01/06 by Alex S. Arvanitakis, Arvanitakis, Alex S., David Tennyson +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2301.02670

openalex publication_date 2023/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a technique to realise brane wrapping and double dimensional reduction in the context of AKSZ topological sigma models and also in their target spaces, which are symplectic L_n-algebroids (i.e. QP-manifolds). Our procedure involves a novel coisotropic reduction combined with an AKSZ transgression that realises degree-shifting; the reduced QP-manifold depends on topological data of the `wrapped' cycle. We check our procedure against the known rules for fluxes under wrapping in the context of M-theory/type IIA duality, and we also find a new relation between Courant algebroids and Poisson manifolds.

Related

• Twisted R-Poisson Sigma Models
• Generalizing Geometry - Algebroids and Sigma Models
• Higher dimensional Lie algebroid sigma model with WZ term
• Doubled Formalism, Complexification and Topological Sigma-Models
• A construction of observables for AKSZ sigma models