Numerical solution of open string field theory in Schnabl gauge

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 $L\le 10$ to estimate the vacuum energies for $L>10$, we predict that the energy reaches a minimum value at $L \sim 12$,andthenturnsbacktoapproach$-1$asymptoticallyas$L \rightarrow \infty$. 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 $L\to \mathrm{\infty }$.