Instantons on noncommutative \(\mathbb{R}^4\), and \((2,0)\) superconformal six dimensional theory. (English) Zbl 0923.58062

Nekrasov, Nikita; Schwarz, Albert

Commun. Math. Phys. 198, No. 3, 689-703 (1998).

Summary: We show that the resolution of the moduli space of ideal instantons parametrizes the instantons on noncommutative \(\mathbb{R}^4\). This moduli space appears to be the Higgs branch of the theory of \(k\) \(D0\)-branes bound to \(N\) \(D4\)-branes by the expectation value of the \(B\) field. It also appears as a regularized version of the target space of supersymmetric quantum mechanics arising in the light cone description of \((2,0)\) superconformal theories in six dimensions.

MSC:

58Z05	Applications of global analysis to the sciences
81T40	Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81Q60	Supersymmetry and quantum mechanics
46L85	Noncommutative topology
46L87	Noncommutative differential geometry

Keywords:

noncommutative geometry; resolution of moduli space; instantons; supersymmetric quantum mechanics; superconformal theories