On stringy AdS5×S5and higher spin holography

We derive the spectrum of Kaluza-Klein descendants of string excitations onAdS_5 x S^5. String states are organized in long multiplets of the AdSsupergroup SU(2,2|4,R) with a rich pattern of shortenings at the higher spinenhancement point \lambda=0. The string states holographically dual to thehigher spin currents of SYM theory in the strict zero coupling limit areidentified together with the corresponding Goldstone particles responsible forthe Higgsing of the higher spin symmetry at \lambda\neq 0. Exploiting higherspin symmetry we propose a very simple yet effective mass formula and establisha one-to-one correspondence between the complete spectrum of \Delta_0 <= 4string states and relevant/marginal single-trace deformations in N=4 SYM theoryat large N. To this end, we describe how to efficiently enumerate scalingoperators in `free' YM theory, with the inclusion of fermionic `letters', byresorting to Polya theory. Comparison between the spectra of 1/4-BPS states isalso presented. Finally, we discuss how to organize the spectrum of N=4 SYMtheory in SU(2,2|4,R) supermultiplets by means of some kind of `Eratostenes'ssieve'.Comment: 38 pages, LateX2e, references adde