Cancellation of linearised axion-dilaton self interaction divergence in strings

Abstract

The force densities exerted on a localised material system by linearised interaction with fields of axionic and dilatonic type are shown to be describable very generally by relatively simple expressions that are well behaved for fields of purely external origin, but that will be subject to ultraviolet divergences requiring regularisation for fields arising from self interaction in submanifold supported ``brane'' type systems. In the particular case of 2-dimensionally supported, i.e. string type, system in an ordinary 4-dimensional background it is shown how the result of this regularisation is expressible in terms of the worldsheet curvature vector $K^μ$, and more particularly that (contrary to what was suggested by early work on this subject) for a string of Nambu Goto type the divergent contribution from the dilatonic self action will always be directed oppositely to its axionic counterpart. This makes it possible for the dilatonic and axionic divergences to entirely cancel each other out (so that there is no need of a renormalisation to get rid of ``infinities'') when the relevant coupling coefficents are related by the appropriate proportionality condition provided by the low energy limit of superstring theory.