Experimental String Field Theory

TL;DR

This paper develops efficient algorithms for level-truncation in open bosonic string field theory, providing numerical solutions up to level 18, extrapolating to higher levels, and confirming the convergence of the approximation scheme.

Contribution

It introduces new algorithms for level-truncation computations and demonstrates convergence of solutions in open bosonic string field theory.

Findings

Energy of the stable vacuum approaches -1 as level increases

Solutions up to level 18 match predictions and extrapolations

Numerical solutions satisfy full gauge-invariant equations of motion

Abstract

We develop efficient algorithms for level-truncation computations in open bosonic string field theory. We determine the classical action in the universal subspace to level (18,54) and apply this knowledge to numerical evaluations of the tachyon condensate string field. We obtain two main sets of results. First, we directly compute the solutions up to level L=18 by extremizing the level-truncated action. Second, we obtain predictions for the solutions for L > 18 from an extrapolation to higher levels of the functional form of the tachyon effective action. We find that the energy of the stable vacuum overshoots -1 (in units of the brane tension) at L=14, reaches a minimum E_min = -1.00063 at L ~ 28 and approaches with spectacular accuracy the predicted answer of -1 as L -> infinity. Our data are entirely consistent with the recent perturbative analysis of Taylor and strongly support the idea that level-truncation is a convergent approximation scheme. We also check systematically that our numerical solution, which obeys the Siegel gauge condition, actually satisfies the full gauge-invariant equations of motion. Finally we investigate the presence of analytic patterns in the coefficients of the tachyon string field, which we are able to reliably estimate in the L -> infinity limit.