String Theory Journal Club

We consider "fool's crowns"' – parts of Riemann surfaces with holes with n marked points/bordered cusps on a hole boundary decorated by horocycles. We define volumes of the corresponding moduli spaces by postulating a decoration-independent action, which in the limit of n tending to infinity transforms into a Schwarzian action on boundary "trumpets". We derive the corresponding volumes for arbitrary n and coupling constant kappa and describe the statistical model obtained in terms of Brownian bridges. This is a joint work with Timothy Budd (Nijmegen Univ.).