Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation

TL;DR

This paper derives equations for the tachyon field on non-BPS D-branes in superstring field theory, constructs a time-dependent rolling tachyon solution, and analyzes energy and pressure evolution during the process.

Contribution

It introduces a specific time-dependent solution for the rolling tachyon in superstring field theory and examines energy conservation and pressure behavior over time.

Findings

The solution describes tachyon rolling from perturbative to stable vacuum.

Energy functional components dominate at different evolution stages.

Pressure reaches zero at minimum and approaches negative energy at infinite time.

Abstract

We derive equations of motion for the tachyon field living on an unstable non-BPS D-brane in the level truncated open cubic superstring field theory in the first non-trivial approximation. We construct a special time dependent solution to this equation which describes the rolling tachyon. It starts from the perturbative vacuum and approaches one of stable vacua in infinite time. We investigate conserved energy functional and show that its different parts dominate in different stages of the evolution. We show that the pressure for this solution has its minimum at zero time and goes to minus energy at infinite time.