Moment-Problem Bounds on OPE Data in Conformal Field Theory
Reformulates the operator product expansion of a conformal four-point correlator as a classical Stieltjes moment problem, so that crossing symmetry and unitarity become two-sided bounds on the moments of the OPE spectral density in scaling dimension and spin. The moment sequences that saturate these bounds are generalized-free-field saddle points of the crossing equations, which can be perturbed to predict the OPE coefficients of double-twist operators in the heavy limit.
2501.00092
We study the operator product expansion (OPE) of identical scalars in a conformal four-point correlator as a Stieltjes moment problem, and use Riemann-Liouville type fractional differential operators…