Test of Siegel Gauge for the Lump Solution

TL;DR

This paper investigates whether the Siegel gauge is a valid choice for the lump solution in cubic open bosonic string field theory by checking the equations of motion for fields outside the gauge, within a modified level truncation at radius $R=\sqrt{3}$ and level $(3,6)$. By computing the linear and quadratic contributions $L$ and $Q$ to the outside-gauge equations of motion and evaluating them on the lump solution, the authors find that $L$ and $Q$ cancel to about $10$–$20\%$ of $L$, indicating approximate agreement with the full, gauge-invariant dynamics. This provides evidence that the lump solution obtained in Siegel gauge satisfies the full equations of motion, analogous to prior checks of BRST invariance for the vacuum. The results support the reliability of Siegel-gauge constructions for nonperturbative configurations and suggest that higher-level truncations should further improve the cancellations, as observed in vacuum analyses.

Abstract

We test the validity of the Siegel gauge condition for the lump solution of cubic open bosonic string field theory by checking the equations of motion of the string field components outside the Siegel gauge. At level (3,6) approximation, the linear and quadratic terms of the equations of motion of these fields are found to cancel within about 20%.