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Multisymplectic geometry is a generalization of symplectic geometry suitablefor n-dimensional field theories, in which the nondegenerate 2-form ofsymplectic geometry is replaced by a nondegenerate (n+1)-form. The case n = 2is relevant to string theory: we call this 2-plectic geometry. Just as thePoisson bracket makes the smooth functions on a symplectic manifold into a Liealgebra, the observables associated to a 2-plectic manifold form a "Lie2-algebra", which is a categorified version of a Lie algebra. Any compactsimple Lie group G has a canonical 2-plectic structure, so it is natural towonder what Lie 2-algebra this example yields. This Lie 2-algebra isinfinite-dimensional, but we show here that the sub-Lie-2-algebra ofleft-invariant observables is finite-dimensional, and isomorphic to the alreadyknown "string Lie 2-algebra" associated to G. So, categorified symplecticgeometry gives a geometric construction of the string Lie 2-algebra.

Categorified Symplectic Geometry and the String Lie 2-Algebra