# Numerical solution for tachyon vacuum in the Schnabl gauge

## TL;DR

This paper develops a numerical method to evaluate the tachyon vacuum in the Schnabl gauge using level truncation up to level 24, confirming theoretical predictions and analyzing various invariants and coefficients.

## Contribution

A new numerical approach for solving the tachyon vacuum in Schnabl gauge with high-level truncation, including energy extrapolation and invariant analysis.

## Key findings

- Energy approaches the analytical value of -1 with increasing level
- Ellwood invariant converges monotonically to the expected value
- Solution coefficients and vacuum expectation values are analyzed for consistency

## Abstract

Based on the level truncation scheme, we develop a new numerical method to evaluate the tachyon vacuum solution in the Schnabl gauge up to level $L=24$. We confirm the prediction that the energy associated to this numerical solution has a local minimum at level $L=12$. Extrapolating the energy data of $L \leq 24$ to infinite level, we observe that the energy goes towards the analytical value $-1$, nevertheless the precision of the extrapolation is lower than in the Siegel gauge. Furthermore, we analyze the Ellwood invariant and show that its value converges monotonically towards the expected analytical result. We also study the tachyon vacuum expectation value (vev) and some other coefficients of the solution. Finally, some consistency checks of the solution are performed, and we briefly discuss the search for other Schnabl gauge numerical solutions.