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

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.

26 pages + appendix, 3 figures

References in corpus (11)

• The BMS/GCA correspondence
• Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Entanglement entropy in Galilean conformal field theories and flat holography
• Dynamics of Carroll Particles
• AdS Witten Diagrams to Carrollian Correlators
• One-loop partition function of three-dimensional flat gravity
• The nuts and bolts of the BMS Bootstrap
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Flavored N=4 SYM -- a highly entangled quantum liquid
• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$