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Concept# Hitchin functional

Summary

The Hitchin functional is a mathematical concept with applications in string theory that was introduced by the British mathematician Nigel Hitchin. and are the original articles of the Hitchin functional.
As with Hitchin's introduction of generalized complex manifolds, this is an example of a mathematical tool found useful in mathematical physics.
Formal definition
This is the definition for 6-manifolds. The definition in Hitchin's article is more general, but more abstract.
Let M be a compact, oriented 6-manifold with trivial canonical bundle. Then the Hitchin functional is a functional on 3-forms defined by the formula:
: \Phi(\Omega) = \int_M \Omega \wedge * \Omega,
where \Omega is a 3-form and * denotes the Hodge star operator.
Properties

- The Hitchin functional is analogous for six-manifold to the Yang-Mills functional for the four-manifolds.
- The Hitchin functional is manifestly invariant under the action of t

Official source

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