Open String States around a Classical Solution in Vacuum String Field Theory

TL;DR

This paper constructs a classical solution in vacuum string field theory, identifies open string states around it, and analyzes their properties, including the tachyon mass and potential height, with high-precision numerical results.

Contribution

It presents a new classical solution in VSFT as a squeezed state, fixing the BRST operator coefficients and analyzing fluctuation modes.

Findings

Tachyon mass squared matches expected value of -1 with high precision.

Potential height ratio to D25-brane tension is computed from Neumann coefficients.

Level truncation behavior of the potential height shows subtle discrepancies.

Abstract

We construct a classical solution of vacuum string field theory (VSFT) and study whether it represents the perturbative open string vacuum. Our solution is given as a squeezed state in the Siegel gauge, and it fixes the arbitrary coefficients in the BRST operator in VSFT. We identify the tachyon and massless vector states as fluctuation modes around the classical solution. The tachyon mass squared \alpha m_t^2 is given in a closed form using the Neumann coefficients defining the three-string vertex, and it reproduces numerically the expected value of -1 to high precision. The ratio of the potential height of the solution to the D25-brane tension is also given in terms of the Neumann coefficients. However, the behavior of the potential height in level truncation does not match our expectation, though there are subtle points in the analysis.