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

TL;DR

This paper links the spectrum of 1/8 BPS states in N=4 Yang-Mills theory to a quantized geometric space of giant gravitons, showing it remains stable across coupling regimes.

Contribution

It introduces a regulated geometric framework for giant gravitons and demonstrates the Hilbert space of these states matches the classical chiral ring, indicating no further renormalization.

Findings

Hilbert space of giant gravitons is isomorphic to the chiral ring

Spectrum of 1/8 BPS states is stable across coupling

Quantization yields a Bose particle model in 3D harmonic oscillator

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.