Global conformal gauge in string theory

TL;DR

This paper proves that the conformal gauge, previously assumed to exist globally in string theory, indeed exists globally on an infinite strip worldsheet, challenging longstanding assumptions in the field.

Contribution

It provides a rigorous proof of the global existence of the conformal gauge on an infinite strip, extending the local results known for string worldsheets.

Findings

Conformal gauge exists globally on an infinite strip worldsheet.

Previous assumptions about global existence were unproven.

The result applies to worldsheets with straight parallel boundaries.

Abstract

It was supposed for fifty years that the conformal gauge in string theory exists globally on the whole string world sheet. In fact, almost all results were obtained under this assumption. However, this statement was proved only locally in some neighbourhood of an arbitrary point on the worldsheet, and its extension is far from being obvious. In the present paper we prove that the conformal gauge does exists globally on the string worldsheet represented by an infinite strip with straight parallel boundaries.