Use in String Theory
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.Grimm & Louis (2004)
As application to string theory, the famous OSV conjecture Ooguri, Strominger & Vafa (2004) used Hitchin functional in order to relate topological string to 4-dimensional black hole entropy. Using similar technique in the holonomy Dijkgraaf et al. (2004) argued about topological M- theory and in the holonomy topological F-theory might be argued.
More recently, E. Witten claimed the mysterious superconformal field theory in six dimensions.Witten (2007)
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