Far beyond the planar limit in strongly-coupled N = 4 SYM

Shai M. Chester, Silviu S. Pufu

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48 Scopus citations


When the SU(N) N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an N = 2-preserving mass parameter m, its free energy F (m, τ,τ¯) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ∂m4F(mττ¯)|m=0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative ∂τ∂τ¯∂m2F(mττ¯)|m=0, and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the N = 4 SYM correlator at separated points. In particular, we determine the leading large-λ term in the N = 4 SYM correlation function at order 1/N8. This is three orders beyond the planar limit.

Original languageEnglish (US)
Article number103
JournalJournal of High Energy Physics
Issue number1
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • 1/N Expansion
  • AdS-CFT Correspondence
  • Extended Supersymmetry


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