Causal Properties of Free String Field Theory

TL;DR

This paper investigates the causal structure of free string field theory, demonstrating that the commutator vanishes at spacelike separations and discussing implications for black hole information paradox solutions.

Contribution

It shows that the commutator of string fields vanishes at spacelike separation, extending the causality results to superstring theory and linking to black hole information issues.

Findings

Commutator vanishes when the integral of squared variations is negative.

Finite mass string field commutator vanishes at spacelike separation.

Results extend to superstring theory, supporting causality in string fields.

Abstract

This paper examines the causal structure of the commutator of two string fields, in free light-cone string field theory. By treating the commutator as a distribution on infinite dimensional loop space, it is shown that the commutator vanishes when $\int d\ss (\delta X(\ss))^2 <0$. Of more direct physical interest is the commutator of finite mass fields, obtained by smearing the string fields with appropriate wave functions. This is shown to vanish at spacelike separations, reproducing the usual point particle field theory result. The implications of this for the information spreading mechanism proposed by Susskind to solve the black hole information problem are discussed. Finally, it is verified that the above conclusions also hold for the superstring.