TY - JOUR

T1 - Far beyond the planar limit in strongly-coupled N = 4 SYM

AU - Chester, Shai M.

AU - Pufu, Silviu S.

N1 - Publisher Copyright:
© 2021, The Author(s).

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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.

KW - 1/N Expansion

KW - AdS-CFT Correspondence

KW - Extended Supersymmetry

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U2 - 10.1007/JHEP01(2021)103

DO - 10.1007/JHEP01(2021)103

M3 - Article

AN - SCOPUS:85104455894

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

M1 - 103

ER -