Comments on Superstring Interactions in a Plane-Wave Background

TL;DR

This work formulates a generalized factorization for the Neumann coefficients of the Type IIB three-string vertex in a maximally supersymmetric plane-wave background, extending the flat-space result to nonzero mass parameter $\mu$. It introduces and exploits the central quantities $\Gamma_+$, $Y=\Gamma_+^{-1}B$, and $k=B^T\Gamma_+^{-1}B$, deriving a $\mu\neq 0$ Neumann coefficient expression in terms of these objects. An involution relates the $\mu>0$ and $\mu<0$ regimes, providing consistency checks for the formalism. The paper also develops the leading large-$\mu$ asymptotics of $\Gamma_+^{-1}$, $Y$, and $k$, outlining constraints (such as $a_R a_k = 1/64$) and highlighting unresolved issues (notably the explicit forms of $Y$ and $k$ and the regulator-dependent value of a parameter $x$) critical for precise gauge theory comparisons.

Abstract

The three string vertex for Type IIB superstrings in a maximally supersymmetric plane-wave background is investigated. Specifically, we derive a factorization theorem for the Neumann coefficients that generalizes a flat-space result that was obtained some 20 years ago. The resulting formula is used to explore the leading large mu asymptotic behavior, which is relevant for comparison with dual gauge theory results.