2022/02/11 by Vincenzo Emilio Marotta, Richard J. Szabo, Marotta, Vincenzo Emilio +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane cosmology #Conformal map #Covariant transformation #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry #Hermitian matrix #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.2202.05680
37 pages; v2: minor corrections, references added; v3: minor changes; Final version to appear in the Special Issue of Universe on "Dualities and Geometry"
openalex publication_date 2022/02/11 · arxiv created 2022/03/21 · arxiv updated 2022/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string version of the Born sigma-model, where they are given by maximally isotropic vector bundles which do not generally admit the standard geometric picture in terms of submanifolds. When reduced to the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold, integrable branes yield D-branes as leaves of foliations which are interpreted as Dirac structures on the physical spacetime. We define a notion of generalised para-complex D-brane, which realises our D-branes as para-complex versions of topological A/B-branes. We illustrate how our formalism recovers standard D-branes in the explicit example of reductions from doubled nilmanifolds.