The Hitchin functional is a mathematical concept with applications in string theory that was introduced by the British mathematician Nigel Hitchin.[1]
As with Hitchin's introduction of generalized complex manifolds, this is an example of a mathematical tool found useful in theoretical physics.
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This is the definition for 6-manifolds. The definition in Hitchin's article is more general, but more abstract.
Let be a compact, oriented 6-manifold with trivial canonical bundle. Then the Hitchin functional is a functional on 3-forms defined by the formula:
where is a 3-form and * denotes the Hodge star operator.
Hitchin functionals arise in many areas of string theory. An example is the compactifications of the 10-dimensional string with a subsequent orientifold projection using an involution . In this case, is the internal 6 (real) dimensional Calabi-Yau space. The couplings to the complexified Kähler coordinates is given by
The potential function is the functional , where J is the almost complex structure. Both are Hitchin functionals.[2]