Open string field theory without open strings

TL;DR

Open bosonic string theory faces a perturbative instability due to a tachyon; the paper tests Sen's conjecture that condensation leads to a stable (closed string) vacuum with no open-string excitations by analyzing level-truncated Witten's cubic open SFT around the nonperturbative vacuum. The authors compute the full scalar sector up to level (6,12), construct the shifted BRST operator tilde Q, and study its cohomology by identifying tilde Q-closed states and their tilde Q-exact partners. Across truncations (0,0), (2,6), (4,12), (6,12), they find that almost all tilde Q-closed states are tilde Q-exact below the cutoff, leaving no physical open-string states and supporting the identification of the stable vacuum with the closed-string vacuum. The results provide strong evidence for Sen's conjecture and motivate further work on relating open SFT to closed-string dynamics and exploring possible pure-ghost forms of the BRST operator.

Abstract

Witten's cubic open string field theory is expanded around the perturbatively stable vacuum, including all scalar fields at levels 0, 2, 4 and 6. The (approximate) BRST cohomology of the theory is computed, giving strong evidence for the absence of physical open string states in this vacuum.

Figures (1)

• Figure 1: Spectrum of $\tilde{Q}$-closed states in level truncations (0, 0), (2, 6), (4, 12) and (6, 12). States below the cutoff $M^2 = L-1$ lie mostly in the exact subspace, confirming Sen's conjecture