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Multi-Instantons and Maldacena's Conjecture

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arxiv hep-th/9810243 v3 pith:YLNNYIJN submitted 1998-10-30 hep-th hep-ph

Multi-Instantons and Maldacena's Conjecture

classification hep-th hep-ph
keywords conjecturek-instantonlarge-nmaldacenaableagreementbulk-to-boundarycalculations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We examine certain n-point functions G_n in {\cal N}=4 supersymmetric SU(N) gauge theory at the conformal point. In the large-N limit, we are able to sum all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of AdS_5 x S^5. (2) In exact agreement with type IIB superstring calculations, at the k-instanton level, $G_n = \sqrt{N} g^8 k^{n-7/2} e^{-8\pi^2 k/g^2}\sum_{d|k} d^{-2} \times F_n(x_1,...,x_n)$, where F_n is identical to a convolution of n bulk-to-boundary SUGRA propagators.

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