Abstract
We study asymptotics of three point coefficients (light-light-heavy) and two point correlators in heavy states in unitary, compact 2D 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. This mimics the scenario of bounds on asymptotic density of states and thereby pronounces an universal feature in asymptotics of 2D CFTs. Next, we clarify the role of smearing in interpreting the asymptotic results pertaining to considerations of eigenstate thermalization in 2D CFTs. In the context of light-light-heavy three point coefficients, we find that the order one number in the bound is sensitive to how close the light operators are from the frac{c}{32} threshold. In context of two point correlator in heavy state, we find the presence of an enigmatic regime which separates the AdS3 thermal physics and the BTZ black hole physics. Furthermore, we present some new numerical results on the behaviour of spherical conformal block.
Highlights
In context of two point correlator in heavy state, we find the presence of an enigmatic regime which separates the AdS3 thermal physics and the BTZ black hole physics
In analyzing 2 point correlator of light operators in heavy states in the large c CFTs, one applies the monodromy method to obtain the vacuum block and in a certain kinemetical configuration it is argued that the vacuum block dominates
Once we appreciate the conceptual parallelism between these two scenarios, we can use our recently understood refined knowledge about Cardy formula to understand the subtle features of general asymptotics in 2D CFT
Summary
The notion of spectral gap for the analysis on (h, h) plane requires more sophistication. Given any elliptical region with semiminor axis of length a > 2, parallel to h = 0 or h = 0 line, centered at (h, h); as the center approaches ∞, the ellipse always contains states a√ppearing in the intermediate channel upon fusing O with O Given any elliptical region with semiminor axis of length a > 2, parallel to fixed spin line or its perpendicular, centered at (h, h); as the center approaches ∞, the ellipse always contains states ap√pearing in the intermediate channel upon fusing O with O.
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