Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Courant algebroids from categorified symplectic geometry   In categorified symplectic geometry, one studies the categorified algebraic
and geometric structures that naturally arise on manifolds equipped with a
closed nondegenerate (n+1)-form. The case relevant to classical string theory
is when n=2 and is called "2-plectic geometry". Just as the Poisson bracket
makes the smooth functions on a symplectic manifold into a Lie algebra, there
is a Lie 2-algebra of observables associated to any 2-plectic manifold. String
theory, closed 3-forms and Lie 2-algebras also play important roles in the
theory of Courant algebroids. Courant algebroids are vector bundles which
generalize the structures found in tangent bundles and quadratic Lie algebras.
It is known that a particular kind of Courant algebroid (called an exact
Courant algebroid) naturally arises in string theory, and that such an
algebroid is classified up to isomorphism by a closed 3-form on the base space,
which then induces a Lie 2-algebra structure on the space of global sections.
In this paper we begin to establish precise connections between 2-plectic
manifolds and Courant algebroids. We prove that any manifold M equipped with a
2-plectic form omega gives an exact Courant algebroid E_omega over M with
Severa class [omega], and we construct an embedding of the Lie 2-algebra of
observables into the Lie 2-algebra of sections of E_omega. We then show that
this embedding identifies the observables as particular infinitesimal
symmetries of E_omega which preserve the 2-plectic structure on M.

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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th