Causality in Covariant String Field Theory

TL;DR

This paper investigates causality in covariant open and closed string field theories, revealing that causality conditions mirror those in light-cone gauge formulations and are invariant under certain transformations.

Contribution

It demonstrates that causality conditions in covariant string field theory are equivalent to those in light-cone gauge and are invariant under sigma shifts, clarifying causality in covariant SFT.

Findings

Causality condition for open SFT matches light-cone gauge results.

Causality condition for closed SFT is sigma-shift invariant.

The causality condition involves the integral of the squared difference of string configurations.

Abstract

Causality is studied in the covariant formulation of free string field theory (SFT). We find that, though the string field in the covariant formulation is a functional of the ghost coordinates as well as the space-time coordinate and the latter contains the time-like oscillators with negative norm, the condition for the commutator of two open string fields to vanish is simply given by $\int_0^\pi d\sigma\left(\Delta X^\mu(\sigma)\right)^2 >0$, which is the same condition as in the light-cone gauge SFT. For closed SFT, the corresponding condition is given in a form which is manifestly invariant under the rigid shifts of the $\sigma$ parameters of the two string fields.