Numerical solution for tachyon vacuum in the Schnabl gauge

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 ≤ 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.

Level Truncation Approach to Open String Field Theory

“…In this chapter, we describe our computer algorithms which we used to obtain the results in this thesis and in some of our previous works [75][14] [76][71][57] [77]. Some parts of these algorithms have already been described in [57][77] and some were inspired by [49].…”

“…Next, we will discuss how to adapt Newton's method to incorporate nontrivial gauge fixing conditions. This algorithm is based on [77].…”

“…Numerical calculations in the level truncation scheme give us only finite level data, which often change quite a lot with level, and therefore we cannot expect that they would have very good precision. However, it has been established that one can significantly improve the precision of results by extrapolating them to infinite level (see for example [84][49] [71][57] [77]).…”

“…This solution have been studied extensively both numerically [86] [95]. We do not have any new results concerning this solution and therefore we will just review its properties following [57] and [77].…”

$KBc$ algebra and the gauge invariant overlap in open string field theory

“…In this section, we are going to study the analytic computation of the gauge invariant overlap for solutions given in terms of elements in the KBc algebra. This gauge invariant observable has been considered in references [11,12,13,15,20,21]. For a given solution Ψ of the string field equations of motion, the gauge invariant overlap is defined as the evaluation of the quantity…”