We study conformal field theory correlation functions relevant For string d
iagrams with open strings that stretch between several parallel branes of d
ifferent dimensions. In the framework of conformal field theory, they invol
ve boundary condition changing twist fields which intertwine between Neuman
n and Dirichlet conditions, A Knizhnik-Zamolodchikov-like differential equa
tion for correlators of such boundary twist fields and ordinary string vert
ex operators is derived, and explicit integral formulas for its solutions a
re provided, (C) 2000 Elsevier Science B.V. All rights reserved.