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

TL;DR

The work develops heavy-light conformal blocks for 2d Carrollian/Galilean CFTs at large $c_M$, showing that under appropriate limits these blocks reduce to global blocks via a conformal transformation that absorbs backreaction. Using the replica trick, the authors derive the entanglement entropy of highly excited states, finding a thermal form when the boost charge crosses a threshold, consistent with ETH in CCFTs. They establish an exact holographic match with swing-surface entanglement entropy in 3D flat space, mapping boundary data $(\Delta,\xi)$ to bulk quantities $(m,j)$ and providing a concrete Flat/CCFT dictionary. The results reinforce flat space holography by connecting boundary conformal blocks, entanglement entropy, and bulk geometries such as spinning particles and Flat Space Cosmologies.

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 $Δ$ and charge $ξ$ 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.

Figures (2)

• Figure 1: Logical flow of this paper
• Figure 3: The geometric construction of the swing surface. The entanglement entropy of the boundary interval $A = [p_1, p_2]$ at null infinity $\mathscr{I}$ is given by the length of the bulk spacelike geodesic $\gamma$ (the swing), which connects to the endpoints of $A$ via two null geodesics $\gamma_\pm$ (dashed orange).