On stringy AdS_5 x S^5 and higher spin holography

TL;DR

The paper builds a string-theoretic, HS-driven framework for AdS5×S5 by deriving KK towers of string excitations, organizing them into SU(2,2|4) multiplets, and applying a simple mass-dimension relation at zero coupling. It then computes the free ${\cal N}=4$ SYM spectrum using Polya theory and shows a precise correspondence for all relevant and marginal operators with $\Delta_0\le 4$, supporting a tensionless-string/HS-AdS/CFT picture. Shortening patterns (BPS/semishort) and Goldstone multiplets illuminate how HS currents and their Higgsing are realized, and an Eratostene-like sieve provides a practical method to identify superprimaries. The results strongly suggest a consistent bridge between tensionless string dynamics in AdS$_5$ and the HS-enhanced symmetry of free SYM, while signaling the need to refine the mass formula for higher-spin and higher-twist sectors and to incorporate interactions. Overall, the work motivates further exploration of HS multiplets, integrability, and holographic duals beyond supergravity.

Abstract

We derive the spectrum of Kaluza-Klein descendants of string excitations on AdS_5 x S^5. String states are organized in long multiplets of the AdS supergroup SU(2,2|4,R) with a rich pattern of shortenings at the higher spin enhancement point λ=0. The string states holographically dual to the higher spin currents of SYM theory in the strict zero coupling limit are identified together with the corresponding Goldstone particles responsible for the Higgsing of the higher spin symmetry at λ\neq 0. Exploiting higher spin symmetry we propose a very simple yet effective mass formula and establish a one-to-one correspondence between the complete spectrum of Δ_0 <= 4 string states and relevant/marginal single-trace deformations in N=4 SYM theory at large N. To this end, we describe how to efficiently enumerate scaling operators in `free' YM theory, with the inclusion of fermionic `letters', by resorting to Polya theory. Comparison between the spectra of 1/4-BPS states is also presented. Finally, we discuss how to organize the spectrum of N=4 SYM theory in SU(2,2|4,R) supermultiplets by means of some kind of `Eratostenes's sieve'.