Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: D-branes and Azumaya/matrix noncommutative differential geometry,II:
  Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a
  view toward dynamical fermionic D-branes in string theory   In this Part II of D(11), we introduce new objects: super-$C^k$-schemes and
Azumaya super-$C^k$-manifolds with a fundamental module (or, synonymously,
matrix super-$C^k$-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.

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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th