We find one explicit $L^2$ harmonic form for every Calabi manifold. Calabi manifolds are known to arise in the low energy dynamics of solitons in Yang-Mills theories, and the $L^2$ harmonic form corresponds to the supersymmetric ground state. As the normalizable ground state of a single $U\left(N\right)\mathrm{}$ instanton, it is related to the bound state of a single D0 to multiple coincident D4’s in the noncommutative setting, or equivalently a unit Kaluza-Klein mode in the discrete light cone quantization of fivebrane world-volume theory. As the ground state of non-Abelian massless monopoles realized around a monopole-“antimonopole” pair, it shows how the long range force between the pair is screened in a manner reminiscent of the large N behavior of the quark-antiquark potential found in AdS/CFT correspondence.

• Received 8 October 2001

DOI:https://doi.org/10.1103/PhysRevD.65.065024