Universal Dynamics of Heavy Operators in Boundary CFT$_2$

TL;DR

This paper derives a universal asymptotic formula for boundary operator coefficients in 2D Boundary CFTs, revealing their dependence on boundary entropy and central charge, with implications for holography and black hole physics.

Contribution

It introduces a universal asymptotic expression for boundary OPE coefficients in 2D BCFTs, interpolating between heavy regimes and relating to boundary entropy.

Findings

Universal formula depends only on boundary entropy and central charge.

Asymptotics suggest an extended Eigenstate Thermalization Hypothesis for boundary operators.

Results have applications in AdS3/BCFT2 and black hole models.

Abstract

We derive a universal asymptotic formula for generic boundary conditions for the average value of the bulk-to-boundary and boundary Operator Product Expansion coefficients of any unitary, compact two-dimensional Boundary CFT (BCFT) with $c>1$. The asymptotic limit consists of taking one or more boundary primary operators -- which transform under a single copy of the Virasoro algebra -- to have parametrically large conformal dimension for fixed central charge. In particular, we find a \textit{single} universal expression that interpolates between distinct heavy regimes, exactly as in the case of bulk OPE asymptotics\cite{Collier:2019weq}. The expression depends universally on the boundary entropy and the central charge, and not on any other details of the theory. We derive these asymptotics by studying crossing symmetry of various correlation functions on higher genus Riemann surfaces with open boundaries. Essential in the derivation is the use of the irrational versions of the crossing kernels that relate holomorphic Virasoro blocks in different channels. Our results strongly suggest an extended version of the Eigenstate Thermalization Hypothesis for boundary OPE coefficients, where the hierarchy between the diagonal and non-diagonal term in the ansatz is further controlled by the boundary entropy. We finally comment on the applications of our results in the context of $\text{AdS}_3/\text{BCFT}_2$, as well as on the recent relation of BCFTs with lower dimensional models of evaporating black holes.