A bstract We compute 1 /λ corrections to the fourpoint functions of halfBPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 superYangMills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of KaluzaKlein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to oneloop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in the limit where N is taken to be large while g YM is kept fixed. In this limit, we present a conjecture for the small mass limit of the S 4 partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes.
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Twoloop superstring fivepoint amplitudes. Part II. Low energy expansion and Sduality
A bstract In an earlier paper, we constructed the genustwo amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the α ′ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1) R preserving amplitudes such as for five gravitons, and for U(1) R violating amplitudes such as for one dilaton and four gravitons. At each order in α ′, the coefficients of the effective interactions are given by integrals over moduli space of genustwo modular graph functions, generalizing those already encountered for four external massless states. To leading and subleading orders, the coefficients of the effective interactions D 2 ℛ 5 and D 4 ℛ 5 are found to match those of D 4 ℛ 4 and D 6 ℛ 4 , respectively, as required by nonlinear supersymmetry. To the next order, a D 6 ℛ 5 effective interaction arises, which is independent of the supersymmetric completion of D 8 ℛ 4 , and already arose at genus one. A novel identity on genustwo modular graph functions, which we prove, ensures that up to order D 6 ℛ 5 , the fivepoint amplitudes require only a single new modular graph function in addition to those needed for the fourpoint amplitude. We check that the supergravity limit of U(1) R violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full fivepoint amplitude, and pave the way for understanding Sduality beyond the BPSprotected sector.
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 Award ID(s):
 1914412
 NSFPAR ID:
 10228357
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 2
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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