Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy

TL;DR

This paper computes the entanglement entropy of excited states in 2D Carrollian/Galilean CFTs, showing it matches holographic predictions and supports flat space holography and the Flat/CCFT correspondence.

Contribution

It introduces a novel derivation of heavy-light conformal blocks in large central charge CFTs and demonstrates their role in reproducing holographic entanglement entropy.

Findings

Entanglement entropy of excited states has a thermal form.

Field-theoretic results match holographic computations.

Establishes a dictionary between boundary state parameters and bulk spacetime properties.

Abstract

We advance the study of flat space holography by computing the entanglement entropy of highly excited states in two-dimensional Carrollian/Galilean Conformal Field Theories (C/G CFTs). Our approach is centered on a novel, physically intuitive derivation of the heavy-light conformal block in the large central charge limit, where the backreaction of heavy operators is absorbed by a C/G conformal coordinate transformation. Using this result and the replica trick, we find that the entanglement entropy of highly excited states assumes a thermal form, providing a concrete realization of the Eigenstate Thermalization Hypothesis (ETH). This field-theoretic result perfectly reproduces the holographic entanglement entropy computed via the swing surface proposal in three-dimensional Einstein gravity, for backgrounds corresponding to spinning particles and Flat Space Cosmological solutions. This agreement establishes a precise dictionary relating the weight $\Delta$ and charge $\xi$ of the boundary state to the mass $m$ and angular momentum $j$ of the dual spacetime, offering a powerful consistency check for the Flat/CCFT correspondence.