Off-shell amplitudes in string theory and hyperbolic geometry

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. (© 2020 WILEY‐VCH Verlag GmbH and Co. KGaA, Weinheim)