N documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mathcal{N} $$end{document} = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization

摘要

A bstract We compute 1 /λ corrections to the four-point functions of half-BPS operators in SU( N ) N documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mathcal{N} $$end{document} = 4 super-Yang-Mills theory at large N and large ’t Hooft coupling λ = g YM 2 N documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {g}_{mathrm{YM}}^2N $$end{document} 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 Kaluza-Klein 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 one-loop 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.