Dilaton Contact Terms in the Bosonic and Heterotic Strings

TL;DR

This paper investigates dilaton contact terms in bosonic and heterotic strings, revealing normalization issues in the bosonic case and proper normalization in the heterotic case, impacting the interpretation of the dilaton as the string coupling.

Contribution

It provides a detailed analysis of dilaton contact terms, highlighting normalization problems in bosonic strings and confirming proper normalization in heterotic strings, with implications for string coupling interpretation.

Findings

Dilaton contact terms are improperly normalized in bosonic strings.

Heterotic strings show properly normalized dilaton contact terms.

The dilaton interpretation as string coupling is valid in heterotic but problematic in bosonic strings.

Abstract

Dilaton contact terms in the bosonic and heterotic strings are examined following the recent work of Distler and Nelson on the bosonic and semirigid strings. In the bosonic case dilaton two-point functions on the sphere are calculated as a stepping stone to constructing a `good' coordinate family for dilaton calculations on higher genus surfaces. It is found that dilaton-dilaton contact terms are improperly normalized, suggesting that the interpretation of the dilaton as the first variation of string coupling breaks down when other dilatons are present. It seems likely that this can be attributed to the tachyon divergence found in \TCCT. For the heterotic case, it is found that there is no tachyon divergence and that the dilaton contact terms are properly normalized. Thus, a dilaton equation analogous to the one in topological gravity is derived and the interpretation of the dilaton as the string coupling constant goes through.