A bstract We study the four-point function of the lowest-lying half-BPS operators in the $$ \mathcal{N} $$ N = 4 SU( N ) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large- N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2 , ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed $$ \mathcal{N} $$ N = 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to N 2 − 1 and are independent of τ and $$ \overline{\tau} $$ τ ¯ , we find that the terms of order $$ \sqrt{N} $$ N and $$ 1/\sqrt{N} $$ 1 / N in the large N expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$more »
Far beyond the planar limit in strongly-coupled $$ \mathcal{N} $$ = 4 SYM
A bstract When the SU( N ) $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an $$ \mathcal{N} $$ N = 2-preserving mass parameter m , its free energy F ( m, τ, $$ \overline{\tau} $$ τ ¯ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ m 4 F m τ τ ¯ m = 0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $$ \mathcal{N} $$ N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the $$ \mathcal{N} $$ N = 4 SYM correlator at separated points. In particular, we determine the leading large- λ term more »
- Award ID(s):
- 1820651
- Publication Date:
- NSF-PAR ID:
- 10311713
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 1
- ISSN:
- 1029-8479
- Sponsoring Org:
- National Science Foundation
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