Symplectic structure in open string field theory I: Rolling tachyons

TL;DR

This paper introduces a new formula for the symplectic structure in open string field theory, applies it to compute energies of rolling tachyon solutions, and compares results with boundary state and scalar field theory analyses.

Contribution

It presents a novel symplectic structure formula for open string field theory and demonstrates its effectiveness in analyzing rolling tachyon solutions and their energies.

Findings

Symplectic structure formula yields consistent energy computations.

Results agree with boundary state calculations.

Scalar field theory analysis provides insights into tachyon oscillations.

Abstract

We discuss a new formula for the symplectic structure on the phase space of open string field theory. Revisiting the setup of Cho, Mazel, and Yin, we use the formula to compute the energy of rolling tachyon solutions on unstable D-branes. An important aspect of the analysis is dealing with the singular ultraviolet behavior of string vertices in Lorentzian signature, a feature we refer to as transgressive locality. This forces us to carry out computations in momentum space, where time and causality are somewhat obscure. Nevertheless the symplectic structure appears to be sensible, giving results in agreement with boundary state computations. As further confirmation of our methods, we study the symplectic structure for rolling tachyons in scalar effective field theory, where vertices show similar high energy behavior to string field theory but the physics is that of local field theory. This model gives interesting insight into the runaway oscillations of the rolling tachyon.