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

Abstract

Mikhailov has constructed an infinite family of (1/8) BPS D3-branes in AdS₅ × S₅. 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 2π 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.