On the exact open-closed vertex in plane-wave light-cone string field theory

The open-closed vertex in the maximally supersymmetric type IIB plane-wave light-cone string field theory is considered and an explicit solution for the bosonic part of the vertex is derived, valid for all values of the mass parameter, \mu. This vertex is of relevance to IIB plane-wave orientifolds, as well as IIB plane-wave strings in the presence of D-branes and their gauge theory duals. Methods of complex analysis are used to develop a systematic procedure for obtaining the solution. This procedure is first applied to the vertex in flat space and then extended to the plane-wave case. The plane-wave solution for the vertex requires introducing certain ``\mu-deformed Gamma functions'', which are generalizations of the ordinary Gamma function. The behaviour of the Neumann matrices is graphically illustrated and their large-\mu asymptotics are analysed.