Universality in asymptotic bounds and its saturation in $2$D CFT

Understand

We study asymptotics of three point coefficients (light-light-heavy) and two point correlators in heavy states in unitary, compact $2$D CFTs.

• We prove an upper and lower bound on such quantities using numerically assisted Tauberian techniques.
• We obtain an optimal upper bound on the spectrum of operators appearing with fixed spin from the OPE of two identical scalars.
• While all the CFTs obey this bound, rational CFTs come close to saturating it.