Supersymmetric states of N=4 Yang-Mills from giant gravitons

Abstract

Mikhailov has constructed an infinite family of 1/8 BPS D3-branes in AdS(5) x S**5. We regulate Mikhailov's solution space by focussing on finite dimensional submanifolds. Our submanifolds are topologically complex projective spaces with symplectic form cohomologically equal to 2 pi N times the Fubini-Study Kahler class. Upon quantization and removing the regulator we find the Hilbert Space of N noninteracting Bose particles in a 3d Harmonic oscillator, a result previously conjectured by Beasley. This Hilbert Space is isomorphic to the classical chiral ring of 1/8 BPS states in N=4 Yang-Mills theory. We view our result as evidence that the spectrum of 1/8 BPS states in N=4 Yang Mills theory, which is known to jump discontinuously from zero to infinitesimal coupling, receives no further renormalization at finite values of the `t Hooft coupling.

66 pages, Latex. v2: typos fixed, references added. v3: more typos and references

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