Timelike modular crossing kernels for N=1 super Liouville theory

Construct the modular and sphere-four-point crossing kernels for N=1 superconformal field theory in the timelike regime of central charges c in (-∞, 3/2], extending the spacelike construction developed for c outside this interval.

Background

The paper constructs all eight modular S-crossing kernels for N=1 super Liouville theory in the spacelike regime, where the central charge lies outside the ray (-∞, 3/2]. The authors note that the corresponding timelike problem is substantially more difficult, even in the bosonic theory, because of the analytic and contour issues associated with timelike Liouville theory.

The unresolved problem is to extend this kernel construction to the timelike N=1 theory, including the appropriate treatment of its NS and Ramond sectors and the associated modular and sphere-four-point crossing transformations.