Numerical solution of open string field theory in Schnabl gauge

TL;DR

This paper numerically investigates open bosonic string field theory in Schnabl gauge using level-truncation methods, predicting the vacuum energy and tachyon vev behavior as the truncation level increases.

Contribution

It provides a detailed numerical analysis of tachyon condensation in Schnabl gauge, extending level-truncation computations up to level 30 and extrapolating results to infinite level.

Findings

Vacuum energy overshoots at level 6 and approaches -1 asymptotically.

Tachyon vev reaches a minimum around level 26 before approaching the analytical value.

Predicted vacuum energy minimum at level ~12, indicating convergence behavior.

Abstract

Using traditional Virasoro $L_0$ level-truncation computations, we evaluate the open bosonic string field theory action up to level $(10,30)$. Extremizing this level-truncated potential, we construct a numerical solution for tachyon condensation in Schnabl gauge. We find that the energy associated to the numerical solution overshoots the expected value $-1$ at level $L=6$. Extrapolating the level-truncation data for $L\leq 10$ to estimate the vacuum energies for $L > 10$, we predict that the energy reaches a minimum value at $L \sim 12$, and then turns back to approach $-1$ asymptotically as $L \rightarrow \infty$. Furthermore, we analyze the tachyon vacuum expectation value (vev), for which by extrapolating its corresponding level-truncation data, we predict that the tachyon vev reaches a minimum value at $L \sim 26$, and then turns back to approach the expected analytical result as $L \rightarrow \infty$.