On stringy AdS_5 x S^5 and higher spin holography

TL;DR

This paper analyzes the spectrum of string excitations on AdS_5 x S^5, identifies dual higher spin currents in SYM at zero coupling, and proposes a mass formula linking string states to SYM deformations.

Contribution

It provides a detailed spectrum analysis of string states, identifies dual higher spin currents, and introduces a simple mass formula connecting string states with SYM deformations.

Findings

Spectrum of string excitations organized in supermultiplets.

Identification of dual higher spin currents in SYM.

A proposed mass formula linking string states to SYM deformations.

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 \lambda=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 \lambda\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 \Delta_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'.