Hyperbolic Geometry of Superstring Perturbation Theory

Understand

We explore the hyperbolic structure of the RNS formulation of perturbative superstring theory.

• The aim is to provide a systematic method to explicitly compute on-shell and off-shell closed superstring amplitudes with an arbitrary number of external states and loops.
• Using hyperbolic geometry, we construct gluing-compatible off-shell string measures by giving a set of gluing-compatible local coordinates around external punctures and a gluing-compatible distribution of picture-changing operators.
• These amplitudes satisfy the required off-shell factorization property.