On the spectrum of AdS/CFT beyond supergravity

TL;DR

This work probes the AdS/CFT spectrum beyond supergravity by analyzing string states on $AdS_5\times S^5$ at the HS enhancement point ($g_{YM}=0$) and matching them to free ${\cal N}=4$ SYM single-trace operators. The authors propose a BMN-inspired mass/dimension formula, $\Delta - J = \nu$, to fix the entire string spectrum and use Polya counting with a refined Eratostenes' Supersieve to extract PSU(2,2|4) primaries, uncovering an emergent $SO(10,2)$ symmetry that organizes the full massive spectrum. They verify the AdS/CFT prediction by showing $\mathcal{Z}_{SO(10,2)} = \sum_{\ell=1}^{\infty} (\mathrm{vac}_{\ell} \times \mathrm{vac}_{\ell})$ up to $\Delta=10$ and report perfect agreement between string and SYM spectra. The results suggest a deeper, possibly 12-dimensional symmetry organizing massive states and point toward further links to integrability and higher-spin dynamics at finite coupling.

Abstract

We test the spectrum of string theory on AdS_5 x S^5 derived in hep-th/0305052 against that of single-trace gauge invariant operators in free N=4 super Yang-Mills theory. Masses of string excitations at critical tension are derived by extrapolating plane-wave frequencies at g_{YM}=0 down to finite J. On the SYM side, we present a systematic description of the spectrum of single-trace operators and its reduction to PSU(2,2|4) superconformal primaries via a refined Eratostenes' supersieve. We perform the comparison of the resulting SYM/string spectra of charges and multiplicities order by order in the conformal dimension Δup to Δ=10 and find perfect agreement. Interestingly, the SYM/string massive spectrum exhibits a hidden symmetry structure larger than expected, with bosonic subgroup SO(10,2) and thirty-two supercharges.