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

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.

10 pages, Latex, 2 references added

References in corpus (6)

• The Generalized Stieltjes Transform and Its Inverse
• On the plane-wave cubic vertex
• On the exact open-closed vertex in plane-wave light-cone string field theory
• Open+Closed String Field Theory From Gauge Fields
• Oblique and curved D-branes in IIB plane-wave string theory
• The Three-String Vertex for a Plane-Wave Background

Cited by in corpus (1)

• Light-cone Superstring Field Theory, pp-wave background and integrability properties