Categorified Symplectic Geometry and the String Lie 2-Algebra

Understand

Multisymplectic geometry is a generalization of symplectic geometry suitable for n-dimensional field theories, in which the nondegenerate 2-form of symplectic geometry is replaced by a nondegenerate (n+1)-form.

• The case n = 2 is relevant to string theory: we call this 2-plectic geometry.
• Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, the observables associated to a 2-plectic manifold form a "Lie 2-algebra", which is a categorified version of a Lie algebra.
• Any compact simple Lie group G has a canonical 2-plectic structure, so it is natural to wonder what Lie 2-algebra this example yields.