Renormalization of multiple infinities and the renormalization group in string loops
Abstract
There is a widespread belief that string loop massles divergences may be absorbed into a renormalization of σmodel couplings (spacetime metric and dilaton). The crucial property for this idea to be consistently implemented to arbitrary order in string loops should be the renormalizability of the generating functional for string amplitudes. We make several nontrivial checks of the renormalizability by explicit calculations at genus 1, 2 and 3. The renormalizability becomes nontrivial at the log ^{2}∊ order. We show that the log ^{2} ∊ counterterms are universal (e.g. the same counterterms provide finiteness both of twoloop scattering amplitudes and of the threeloop partition function) and are related to the log ∊ counterterms (βfunctions) in the standard way dictated by the renormalization group. This checks the consistency of the FischlerSusskind mechanism and implies that the renormalization group acts properly at the string loop level.
 Publication:

Nuclear Physics B
 Pub Date:
 August 1990
 DOI:
 10.1016/05503213(90)90159B
 Bibcode:
 1990NuPhB.340..113R