Theorems for the Lightcone Bootstrap

TL;DR

This paper provides a rigorous mathematical proof that, under certain conditions, the spectrum and OPE coefficients of a conformal field theory at large spin and fixed twist asymptotically resemble those of a generalized free field theory.

Contribution

The paper offers a formal proof confirming the asymptotic behavior of spectrum and OPE coefficients in the lightcone bootstrap for conformal field theories.

Findings

Spectrum and OPE coefficients match generalized free field theory at large spin

Proof applies to theories with a discrete spectrum and twist gap

Supports the lightcone bootstrap conjecture in conformal field theory

Abstract

Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE coefficients at large spin and fixed twist always become that of a generalized free field theory.