The N = 4 quantum conformal algebra Original Research Article

We determine the spectrum of currents generated by the operator product expansion of the energy-momentum tensor in N = 4 super-symmetric Yang-Mills theory. Up to the regular terms and in addition to the multiplet of the stress tensor, three current multiplets appear, Σ, Ξ and ϒ starting with spin 0, 2 and 4, respectively. The OPEʹs of these new currents generate an infinite tower of current multiplets, one for each even spin, which exhibit a universal structure, of length 4 in spin units, identified by a two-parameter rational family. Using higher-spin techniques developed recently for conformal field theories, we compute the critical exponents of Σ, Ξ and ϒ in the TT OPE and prove that the essential structure of the algebra holds at arbitrary coupling. We argue that the algebra closes in the strongly coupled large-Nc limit. Our results determine the quantum conformal algebra of the theory and answer several questions that previously remained open.