Siegel Gauge in Vacuum String Field Theory
Kazumi Okuyama
TL;DR
This paper investigates the ghost sector star algebra in vacuum string field theory, revealing BRST exactness of star products in Siegel gauge and introducing a new star product to characterize the equations of motion.
Contribution
It introduces a new star product in the Siegel gauge and characterizes the VSFT equations of motion as a projection condition, advancing understanding of the ghost sector algebra.
Findings
Star product of two states in Siegel gauge is BRST exact.
BRST exact states are nil factors in the star algebra.
New star product characterizes VSFT's equations of motion.
Abstract
We study the star algebra of ghost sector in vacuum string field theory (VSFT). We show that the star product of two states in the Siegel gauge is BRST exact if we take the BRST charge to be the one found in hep-th/0108150, and the BRST exact states are nil factors in the star algebra. By introducing a new star product defined on the states in the Siegel gauge, the equation of motion of VSFT is characterized as the projection condition with respect to this new product. We also comment on the comma form of string vertex in the ghost sector.
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