On the Eleventh Dimension of String Theory

TL;DR

This paper explores the origin of the hidden eleventh dimension in string theory, linking sigma models, Weyl transformations, and Abelian T-duality to clarify the theoretical foundation of the extra dimension.

Contribution

It demonstrates that the eleventh dimension arises from the need to resolve ambiguities in sigma models, connecting it with Weyl transformations and Abelian T-duality.

Findings

Any two sigma models are related by a Weyl transformation.

Extra fields are necessary to define sigma models unambiguously.

A connection between the eleventh dimension and Abelian T-duality is established.

Abstract

An explanation of the origin of the hidden eleventh dimension in string theory is given. It is shown that any two sigma models describing the propagation of string backgrounds are related to each other by a Weyl transformation of the world-sheet metric. To avoid this ambiguity in defining two-dimensional sigma models, extra fields are needed. An interesting connection is established with Abelian T-duality.