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Published April 15, 2003 | public
Journal Article Open

Explicit formulas for Neumann coefficients in the plane-wave geometry


We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter mu. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We derive asymptotic expansions for large mu and find unexpectedly simple results, which are valid to all orders in 1/mu. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified 't Hooft coupling lambda'. A specific example is presented.

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©2003 The American Physical Society. Received 15 January 2003; published 24 April 2003. M.S. and A.V. are grateful to I. Klebanov for collaboration in the early stages of their work on this project, and to D. Freedman and R. Roiban for helpful discussions. The hospitality of Princeton University (A.V.) and the Aspen Center for Physics (J.H.S., M.S. and A.V.), where portions of this work were carried out, is also appreciated. This research was supported in part by the U.S. Dept. of Energy under Grants No. DE-FG02-95ER40893 (Y.H.H.), DE-FG03-92-ER40701 (J.H.S.) and DE-FG02-91ER40671 (M.S.), and by the National Science Foundation under Grant No. PHY99-07949 (A.V.).


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