The N=4 Quantum Conformal Algebra

Abstract

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, Sigma, Xi and Upsilon, starting with spin 0, 2 and 4, respectively. The OPE's 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 Sigma, Xi and Upsilon 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-$N_c$ limit. Our results determine the quantum conformal algebra of the theory and answer several questions that previously remained open.

17 pages, 2 figures. One additional comment on spin hierarchies. Final version, to appear in npb. (v2: The essential structure of the algebra holds at arbitrary coupling)

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• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Higher Spin N=8 Supergravity
• Theory of higher spin tensor currents and central charges
• Bulk Gauge Fields in AdS Supergravity and Supersingletons
• ``Non chiral'' primary superfields in the AdS_{d+1}/CFT_d correspondence

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