Excitations on wedge states and on the sliver

TL;DR

The paper addresses the open-string tachyon vacuum problem in cubic string field theory by analyzing ghost-number-one excitations on the sliver, using the generalized gluing and resmoothing theorem to compute the Witten vertex and kinetic term for excitations on wedge states and in the sliver limit. It develops a similarity-transformation framework to define excitations on wedge states and derives their vertices, then takes the sliver limit to obtain the effective action for ghost-sector excitations up to level two for two BRST choices $Q=c_0$ and $Q=c_0+(c_2+c_{-2})/2$. The results show near-identical maxima of the effective potential across zeroth and second levels for both BRST choices, suggesting convergence of level truncation and supporting the conjectured tachyon-vacuum action; discrete symmetries are preserved in the sliver limit and certain excitations yield well-defined vertices while others do not. Overall, the work provides a concrete, convergent framework for exploring nonperturbative vacua in open SFT and validates the use of sliver-based ghost excitations in testing Sen-like conjectures.

Abstract

We study ghost number one excitations on the sliver to investigate the solution of string field actions around the tachyon vacuum. The generalized gluing and resmoothing theorem is used to develop a method for evaluating the effective action for excitations on both the wedge states and the sliver state. We analyze the discrete symmetries of the resulting effective action for excitations on the sliver. The gauge unfixed effective action till level two excitations on the sliver is evaluated. This is done for the case with the BRST operator $c_0$ and $c_0 + (c_2 + c_{-2})/2$ with excitations purely in the ghost sector. We find that the values of the effective potential at the local maximum lie close by for the zeroth and the second level of approximation. This indicates that level truncation in string field theory around the tachyon vacuum using excitations on the sliver converges for both choices of the BRST operator. It also provides evidence for the conjectured string field theory actions around the tachyon vacuum.