A note on the uniqueness of the Neumann matrices in the plane-wave background

TL;DR

This paper proves the uniqueness of Neumann matrices in plane-wave light-cone string-field theory, establishing that geometric conditions suffice to determine the vertices, with explicit formulas involving mu-deformed Gamma functions.

Contribution

It demonstrates the uniqueness of the Neumann matrices and their inverses in the plane-wave background, providing explicit expressions and using complex analysis techniques.

Findings

Uniqueness of Neumann matrices established for all mu values.

Explicit inverse matrix expressed via mu-deformed Gamma functions.

Geometrical conditions suffice to determine the bosonic vertices.

Abstract

In this note, we prove the uniqueness of the Neumann matrices of the open-closed vertex in plane-wave light-cone string-field theory, first derived for all values of the mass parameter mu in hep-th/0311231. We also prove the existence and uniqueness of the inverse of an infinite dimensional matrix necessary for the cubic vertex Neumann matrices, and give an explicit expression for it in terms of mu-deformed Gamma functions. Methods of complex analysis are used together with the analytic properties of the mu-deformed Gamma functions. One of the implications of these results is that the geometrical continuity conditions suffice to determine the bosonic part of the vertices as in flat space.