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 μ. 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 μ and find unexpectedly simple results, which are valid to all orders in 1/μ. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified ’t Hooft coupling λ^′. A specific example is presented.