Hitchin functional

Hitchin Functional

Hitchin functional

to get instant updates about 'Hitchin Functional' on your MyPage. Meet other similar minded people. Its Free!

X 

All Updates


Description:
The Hitchin functional is a mathematical concept with applications in string theory that was introduced by the British mathematician Nigel Hitchin.

As with Hitchin's introduction of generalized complex manifolds, this is an example of a mathematical tool found useful in theoretical physics.

Formal definition

This is the definition for 6-manifolds. The definition in Hitchin's article is more general, but more abstract.

Let <math>M</math> be a compact, oriented 6-manifold with trivial canonical bundle. Then the Hitchin functional is a functional on 3-forms defined by the formula:

<math>Phi(Omega) = int_M Omega wedge * Omega,</math>


where <math>Omega</math> is a 3-form and * denotes the Hodge star operator.

Properties

  • The Hitchin functional is analogous to the Yang-Mills functional for the four-manifolds.




  • Theorem. Suppose that <math>M</math> is a three-dimensional complex manifold and <math>Omega</math> is the real part of a non-vanishing holomorphic 3-form, then <math>Omega</math> is a critical point of the functional <math>Phi</math> restricted to the cohomology class <math> in H^3(M,R)</math>. Conversely, if......
  • ...

Read More

No feeds found

All
wait Posting your question. Please wait!...


No updates available.
No messages found
Tell your friends >
about this page
 Create a new Page
for companies, colleges, celebrities or anything you like.Get updates on MyPage.
Create a new Page
 Find your friends
  Find friends on MyPage from