Cancellation of Linearized Axion-Dilaton Self-Action Divergence in Strings

The force densities exerted on a localizedmaterial system by linearized interaction with fields ofaxionic and dilatonic type are shown to be describablevery generally by relatively simple expressions that are well behaved for fields of purelyexternal origin, but that will be subject to ultravioletdivergences requiring regularization for fields arisingfrom self-interaction in submanifold-supported brane-type systems. In theparticular case of a two-dimensionally supported, i.e.,string-type, system in an ordinary four-dimensionalbackground it is shown how the result of thisregularization is expressible in terms of the worldsheetcurvature vector K, and more particularlythat (contrary to what was suggested by early work onthis subject) for a string of Nambu-Goto type thedivergent contribution from the dilatonic self-action will always bedirected oppositely to its axionic counterpart. Thismakes it possible for the dilatonic and axionicdivergences entirely to cancel each other out (so that there is no need of a renormalization to getrid of infinities) when the relevantcoupling coefficents are related by the appropriateproportionality condition provided by the low-energylimit of superstring theory.