The Light Cone in String Theory

TL;DR

This paper explores the causal boundary in string theory, defining it through loop space hypersurfaces and discussing potential implications for string propagation and measurement interference.

Contribution

It introduces a novel causal boundary concept in string theory based on loop space hypersurfaces and analyzes its possible consequences.

Findings

Defined the causal boundary as a hypersurface in loop space.

Linked the boundary condition to a specific integral involving string variations.

Discussed potential implications for string measurement and interference.

Abstract

The causal boundary of string propagation -- defined as the hypersurface in loop space bordering the timelike(spacelike) domains in which two successive measurements of the string field do(do not) interfere with one another -- is argued to be $0=\int d\sigma\bigl(\delta X(\sigma)\bigr)^2 = \sum_{\ell=-\infty}^\infty \delta x^\mu_{-\ell}\delta x_{\mu \ell}.$ Some possible consequences are discussed.