The shape of instantons: cross-section of supertubes and dyonic instantons

We explore the correspondence between Yang-Mills instantons and algebraiccurves. The curve is defined by Higgs zero locus of dyonic instantons in 1+4dimensional Yang-Mills-Higgs theory, and it is identified in string theory withthe cross-section of supertubes connecting parallel D4-branes. To presentevidence for the identification, we show that with total charges fixed, thesupertube angular momentum computed from the Higgs zero locus is maximized whenthe locus is circular, which has been proven for the cross-section of thesupertubes. This leads to a consistent dictionary between the charges in twopictures. We also consider a T-dual version of the story, identifying theprofiles of the wavy instanton strings with those of the supercurves/D-helices.Based on this observation, we then argue a novel correspondence between ADHMdata of instantons and algebraic curves defining the locus. The degree of thecurve is related to the instanton number, and splitting property of the curveis physically manifested by well-separated instantons.Comment: 28 pages, 7 figures; a reference adde