ADHM Construction

All Updates

The **ADHM construction** or **monad construction** is the construction of all instantons using method of linear algebra by Michael Atiyah, Vladimir G. Drinfel'd, Nigel. J. Hitchin, Yuri I. Manin in their paper *Construction of Instantons*.

## ADHM data

The ADHM construction uses the following data:

Then ADHM construction claims that, given certain regularity conditions,

## Generalizations

### Noncommutative instantons

In a noncommutative gauge theory, the ADHM construction is identical but the moment map <math>vecmu </math> is set equal to the...

Read More

- complex vector spaces
*V*and*W*of dimension*k*and*N*, -
*k*×*k*complex matrices*B*<sub>1</sub>,*B*<sub>2</sub>, a*k*×*N*complex matrix*I*and a*N*×*k*complex matrix*J*, - a real moment map <math>mu_r = ++II^dagger-J^dagger J</math>,
- a complex moment map <math>displaystylemu_c = +IJ</math>.

Then ADHM construction claims that, given certain regularity conditions,

- Given
*B*<sub>1</sub>,*B*<sub>2</sub>,*I*,*J*such that <math>mu_r=mu_c=0</math>, an Anti-Self-Dual instanton in a SU gauge theory with instanton number*k*can be constructed, - All Anti-Self-Dual instantons can be obtained in this way and are in one-to-one correspondence with solutions up to a U(k) rotation which acts on each
*B*in the adjoint representation and on*I*and*J*via the fundamental and antifundamental representations - The metric on the moduli space of instantons is that inherited from the flat metric on
*B*,*I*and*J*.

Read More

No messages found

about this page

for companies, colleges, celebrities or anything you like.Get updates on MyPage.

Create a new Page