Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM

Abstract

When the $SU(N)$ $\mathcal{N}=4$ super-Yang-Mills (SYM) theory with complexified gauge coupling $\tau$ is placed on a round four-sphere and deformed by an $\mathcal{N}=2$-preserving mass parameter $m$, its free energy $F(m,\tau ,\bar{\tau })$ can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ${\partial }_m^{4}F(m,\tau ,\bar{\tau }){|}_{m=0}$ of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $\mathcal{N}=4$ SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative ${\partial }_{\tau }{\partial }_{\bar{\tau }}{\partial }_m^{2}F(m,\tau ,\bar{\tau }){|}_{m=0}$, and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large $N$ and large 't Hooft coupling $\lambda$ expansion of the $\mathcal{N}=4$ SYM correlator at separated points. In particular, we determine the leading large-$\lambda$ term in the $\mathcal{N}=4$ SYM correlation function at order $1/N^8$. This is three orders beyond the planar limit.

25 pages plus appendices, v2 submitted to JHEP, minor typos fixed

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• Sphere Partition Functions and the Zamolodchikov Metric
• R^4, purified
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence

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