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Level truncation and the tachyon in open bosonic string field theory

The tachyonic instability of the open bosonic string is analyzed using the level truncation approach to string field theory. We have calculated all terms in the cubic action of the string field theory describing zero-momentum interactions of up to level 20 between scalars of level 10 or less. These results are used to study the tachyon effective potential and the nonperturbative stable vacuum. We find that the energy gap between the unstable and stable vacua converges much more quickly than the coefficients of the effective tachyon potential. By including fields up to level 10, 99.91% of the energy from the bosonic D-brane tension is cancelled in the nonperturbative stable vacuum. It appears that the perturbative expansion of the effective tachyon potential around the unstable vacuum has a small but finite radius of convergence. We find evidence for a critical point in the tachyon effective potential at a small negative value of the tachyon field corresponding to this radius of convergence. We study the branch structure of the effective potential in the vicinity of this point and speculate that the tachyon effective potential is globally nonnegative.