Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry

TL;DR

This paper derives explicit formulas for Neumann coefficients in the three-string vertex of type IIB string theory in a plane-wave background, providing new insights and predictions for gauge theory via BMN duality.

Contribution

It presents the first explicit formulas for Neumann coefficients for any mass parameter mu, including asymptotic expansions valid to all orders in 1/mu.

Findings

Explicit formulas for Neumann coefficients derived

Asymptotic expansions for large mu obtained

Predictions for gauge theory quantities to all orders in lambda'

Abstract

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.