Four-point correlation modular bootstrap for OPE densities

In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the vacuum and no conserved currents. For those theories, we compute the large dimension limit (h/c >> 1) of the OPE spectral decomposition of the Virasoro vacuum. We then propose a kernel ansatz that generalizes the spectral decomposition beyond h/c >> 1. Finally, we estimate the corrections to the OPE spectral densities from the inclusion of the lightest operator in the spectrum.

Automated summary

In this work, the lightcone bootstrap was applied to study the four-point function of scalars in two-dimensional conformal field theory, including the entire Virasoro symmetry. A kernel ansatz was proposed to generalize the spectral decomposition of the Virasoro vacuum, extending it beyond the large dimension limit.