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