Supersymmetric states of 𝒩 = 4 Yang-Mills from giant gravitons (original) (raw)

Mikhailov has constructed an infinite family of 1 8 BPS D3-branes in AdS 5 × 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 2πN times the Fubini-Study Kähler 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.