2014/12/02 by Chien‐Hao Liu, Shing–Tung Yau, Liu, Chien-Hao +1 · 1 citation
Mathematics · Physics and Astronomy · #14A22 #16S50 #46L87 #51K10 #58A40 #58A50 #81T30 #81T60 #81T75 #81V22 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1412.0771
openalex publication_date 2014/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this Part II of D(11), we introduce new objects: super-Ck-schemes and Azumaya super-Ck-manifolds with a fundamental module (or, synonymously, matrix super-Ck-manifolds with a fundamental module), and extend the study in D(11.1) ([L-Y3], arXiv:1406.0929 [math.DG]) to define the notion of `differentiable maps from an Azumaya/matrix supermanifold with a fundamental module to a real manifold or supermanifold'. This allows us to introduce the notion of `fermionic D-branes' in two different styles, one parallels Ramond-Neveu-Schwarz fermionic string and the other Green-Schwarz fermionic string. A more detailed discussion on the Higgs mechanism on dynamical D-branes in our setting, taking maps from the D-brane world-volume to the space-time in question and/or sections of the Chan-Paton bundle on the D-brane world-volume as Higgs fields, is also given for the first time in the D-project. Finally note that mathematically string theory begins with the notion of a differentiable map from a string world-sheet (a 2-manifold) to a target space-time (a real manifold). In comparison to this, D(11.1) and the current D(11.2) together bring us to the same starting point for studying D-branes in string theory as dynamical objects.