Off‐Shell Amplitudes in String Theory and Hyperbolic Geometry

Abstract

The construction of off‐shell amplitudes in closed string theory using Riemann surfaces having constant curvature −1 is explored in detail. Off‐shell string amplitudes constructed using surfaces with constant curvature −1 fail to satisfy the off‐shell factorization properties, and as a result, scattering amplitudes computed using them are ill‐defined. In this paper, we describe a procedure for systematically modifying this construction and obtain consistent off‐shell amplitudes in closed string theory satisfying the off‐shell factorization properties.