Cancellation of linearised axion-dilaton self interaction divergence in strings

TL;DR

This paper demonstrates that in string models inspired by superstring theory, the divergent self-interactions of axion and dilaton fields cancel each other out, eliminating the need for renormalization.

Contribution

It shows how the divergent self-interaction terms for axion and dilaton fields on strings can be exactly canceled under superstring low-energy conditions, simplifying the theory.

Findings

Dilatonic and axionic divergences are oppositely directed for Nambu Goto strings.

Divergences cancel when coupling coefficients satisfy superstring low-energy relations.

No renormalization needed due to divergence cancellation in these models.

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 $K^\mu$, 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.