On stringy AdS5 × S5 and higher spin holography

We derive the spectrum of Kaluza-Klein descendants of string excitations on AdS5 × S5. String states are organized in long multiplets of the AdS supergroup SU(2,2|4) 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≠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 Δ0 ≤ 4 string states and relevant/marginal single-trace deformations in = 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 = 4 SYM theory in SU(2,2|4) supermultiplets by means of some kind of `Eratostene's sieve'.