STRING TECHNIQUES FOR THE CALCULATION OF RENORMALIZATION-CONSTANTS IN-FIELD THEORY

We describe a set of methods to calculate gauge theory renormalization constants from string theory, all based on a consistent prescription to continue off-shell open bosonic string amplitudes. We prove the con sistency of our prescription by explicitly evaluating the renormalizat ions of the two-, three- and four-gluon amplitudes, and showing that t hey obey the appropriate Ward identities. The field theory limit thus performed corresponds to the background field method in Feynman gauge, We identify precisely the regions in string moduli space that corresp ond to different classes of Feynman diagrams, and in particular we sho w how to isolate contributions to the effective action. Ultraviolet di vergent terms are then encoded in a single string integral over the mo dular parameter tau, Finally, we derive a multiloop expression for the effective action by computing the partition function of an open boson ic string interacting with an external non-abelian background gauge fi eld.