Is the String Coupling Constant invariant under T-duality?

TL;DR

This paper investigates whether the string coupling constant remains invariant under T-duality, clarifying the apparent discrepancy between different definitions and transformations of the dilaton in string theory.

Contribution

The paper analyzes the relationship between the sigma model dilaton and the string coupling constant under T-duality, resolving conflicting claims in the literature.

Findings

The sigma model dilaton shifts additively under T-duality.

The string coupling constant may be associated with different dilatons in different frameworks.

Clarification of the invariance or non-invariance of the string coupling under T-duality.

Abstract

It is well known that under T-duality the sigma model dilaton (which is normally thought to be related to the string coupling constant through the simple formula $\kappa = exp <\phi >$), undergoes an additive shift. On the other hand, Kugo and Zwiebach, using a simplified form of string field theory, claim that the string coupling constant does not change under the T-duality. Obviously, what seems to happen is that two different coupling constants, associated to different dilatons, are used. In this contribution we shall try to clarify this, and related issues.