Exact classical solutions and tachyon vacuum in closed bosonic string field theory

Construct exact classical solutions of bosonic closed string field theory and establish a convincing identification of its tachyon vacuum. In particular, develop explicit solutions (analogous in spirit to Schnabl’s open-string solution) that satisfy the closed string field theory equations of motion and compute their on-shell action to confirm the expected vacuum structure.

Background

While open string field theory boasts many exact solutions, including the analytic tachyon vacuum, closed bosonic string field theory still lacks known exact classical solutions and a definitive identification of its tachyon vacuum. The polyhedral (Strebel) or hyperbolic vertex constructions provide well-defined frameworks, but explicit nontrivial solutions have remained elusive.

Achieving an exact solution and clarifying the closed-string tachyon vacuum would be a major advance, potentially paralleling the breakthroughs in open string field theory and informing the understanding of vacuum structure and nonperturbative dynamics in the closed sector.