A note on the Einstein equation in string theory

TL;DR

This paper argues that the metric background in string theory must satisfy Einstein-like equations based on classical reasoning, revealing restrictions on worldsheet curvature that influence spacetime gravity.

Contribution

It provides a classical derivation showing that string backgrounds inherently satisfy Einstein or Einstein-like equations, highlighting the geometric constraints on worldsheet curvature.

Findings

Background metric must satisfy Einstein-like equations

Restrictions on worldsheet curvature act as sources for gravity

Classical considerations imply geometric constraints in string theory

Abstract

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein-like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter fields.