DLCQ of Fivebranes, Large N Screening, and L^2 Harmonic Forms on Calabi Manifolds

TL;DR

This paper constructs explicit L^2 harmonic forms on Calabi manifolds, revealing their role in supersymmetric ground states of solitons in gauge theories and illustrating large N screening phenomena similar to AdS/CFT results.

Contribution

It provides explicit L^2 harmonic forms on Calabi manifolds and links these to supersymmetric ground states in gauge theories and string theory contexts.

Findings

Explicit L^2 harmonic form for each Calabi manifold.

Connection between harmonic forms and supersymmetric ground states.

Illustration of large N screening behavior in soliton interactions.

Abstract

We find one explicit L^2 harmonic form for every Calabi manifold. Calabi manifolds are known to arise in 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(N) instanton, it is related to the bound state of a single D0 to multiple coincident D4's in the non-commutative setting, or equivalently a unit Kaluza-Klein mode in DLCQ of fivebrane worldvolume theory. As the ground state of nonabelian massless monopoles realized around a monopole-``anti''-monopole pair, it shows how the long range force between the pair is screened in a manner reminiscent of large N behavior of quark-anti-quark potential found in AdS/CFT correspondence.