P. Divecchia et al., STRING TECHNIQUES FOR THE CALCULATION OF RENORMALIZATION-CONSTANTS IN-FIELD THEORY, Nuclear physics. B, 469(1-2), 1996, pp. 235-286
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.