Hyperbolic string vertices

A bstract The string vertices of closed field theory are subsets the moduli spaces punctured Riemann surfaces that satisfy a geometric version Batalin-Vilkovisky master equation. We present homological proof existence and their uniqueness up to canonical transformations. Using hyperbolic metrics on with geodesic boundaries we give an exact construction as sets systole greater than or equal L ≤ 2 arcsinh 1. Intrinsic collars prevent appearance short geodesics upon sewing. generated by Feynman diagrams naturally endowed Thurston metrics: flat propagators. For classical length is arbitrary and, → ∞ become minimal-area theory.