The N=4 Quantum Conformal Algebra

TL;DR

This paper determines the quantum conformal algebra of N=4 super-symmetric Yang-Mills theory, revealing an infinite tower of current multiplets with universal structure and computing their critical exponents at arbitrary coupling.

Contribution

It identifies the full spectrum of currents generated by the energy-momentum tensor's OPE and demonstrates the algebra's closure at strong coupling, advancing understanding of N=4 SYM.

Findings

Discovery of an infinite tower of current multiplets with even spins

Universal structure of the current algebra with a two-parameter family

Validation of algebra closure at arbitrary coupling and large N_c

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.