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

TL;DR

The paper tackles the finite-$N$, finite-$\lambda$ spectrum of $1/8$ BPS states in $\mathcal{N}=4$ Yang–Mills by quantizing Mikhailov's giant gravitons. By regulating the solution space to finite-dimensional submanifolds $\mathbb{CP}^{n_C-1}$ and showing the symplectic form lives in the cohomology class $[\omega]=(2\pi N)\omega_{FS}$, the authors demonstrate that the resulting Hilbert space is equivalent to $N$ bosons in a 3D harmonic oscillator, matching the $1/8$ BPS chiral ring predicted by the index and supporting nonrenormalization at finite coupling. The analysis unifies geometric quantization with holographic expectations, reproducing the index-based partition function and revealing a robust, regulator-independent structure of the $1/8$ BPS sector. The work also clarifies the roles of dual giants, topology changes in the moduli space, and potential extensions to $1/16$ BPS states and more general geometries, highlighting a deep link between giant gravitons and the SYM chiral ring with broad implications for AdS/CFT and BPS state counting.

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.