Four-point correlation modular bootstrap for OPE densities

TL;DR

This paper develops a bootstrap approach for 2D conformal field theories with Virasoro symmetry, analyzing OPE densities and spectral decompositions in the large dimension limit and beyond, with applications to non-rational theories.

Contribution

It introduces a kernel ansatz for the spectral decomposition of OPE densities in 2D CFTs, extending analysis beyond the large dimension limit and including corrections from lightest operators.

Findings

Computed the large h/c limit of the Virasoro vacuum OPE spectral decomposition.

Proposed a generalized kernel ansatz for spectral decomposition beyond the large h/c regime.

Estimated corrections to OPE spectral densities from the lightest spectrum operators.

Abstract

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.