A bstract We study the fourpoint function of the lowestlying halfBPS operators in the $$ \mathcal{N} $$ N = 4 SU( N ) superYangMills theory and its relation to the flatspace fourgraviton amplitude in type IIB superstring theory. We work in a large N expansion in which the complexified YangMills coupling τ is fixed. In this expansion, nonperturbative 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 massdeformed 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 fourpoint correlator at separated points. In a normalization where the twopoint 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 fourpoint correlator are proportional to the nonholomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$ E\left(\frac{5}{2},\tau, \overline{\tau}\right) $$ E 5 2 τ τ ¯ , respectively. In the flat space limit, these terms match the corresponding terms in the type IIB Smatrix arising from R 4 and D 4 R 4 contact interactions, which, for the R 4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order $$ {N}^{\frac{1}{2}m} $$ N 1 2 − m with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of nonholomorphic Eisenstein series with halfinteger index, which are manifestly SL(2 , ℤ) invariant.
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Strong coupling expansion of circular Wilson loops and string theories in AdS5 × S5 and AdS4 × CP3
A bstract We revisit the problem of matching the strong coupling expansion of the $$ \frac{1}{2} $$ 1 2 BPS circular Wilson loops in $$ \mathcal{N} $$ N = 4 SYM and ABJM gauge theories with their string theory duals in AdS 5 × S 5 and AdS 4 × CP 3 , at the first subleading (oneloop) order of the expansion around the minimal surface. We observe that, including the overall factor 1/ g s of the inverse string coupling constant, as appropriate for the open string partition function with disk topology, and a universal prefactor proportional to the square root of the string tension T , both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the $$ \sqrt{T} $$ T prefactor based on special features of the combination of oneloop determinants appearing in the string partition function. The latter also implies a natural generalization Z χ ∼ ( $$ \sqrt{T}/{g}_{\mathrm{s}} $$ T / g s ) χ to higher genus contributions with the Euler number χ , which is consistent with the structure of the 1/ N corrections found on the gauge theory side.
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 Award ID(s):
 1914860
 NSFPAR ID:
 10206130
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2020
 Issue:
 10
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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