Gravitational anomalies, entanglement entropy, and flat-space holography

TL;DR

The paper develops a framework to compute entanglement entropy (EE) for Galilean conformal field theories (GCFTs) dual to flat-space cosmologies by combining gravitational anomalies with Inönü–Wigner contraction. It derives zero- and finite-temperature GCFT2 EE, reproduces the flat-space Cardy-like behavior in the thermal regime, and provides a holographic FSC EE formula obtained via contraction from BTZ/TMG results, with detailed consistency checks in various limits. The results reinforce the BMS/GCA correspondence as a robust tool in flat-space holography and yield explicit EE expressions across regimes, including Einstein gravity, boost orbifolds, and flat-space chiral gravity. The work opens avenues for geometric derivations of these EE expressions from holographic proposals and for exploring EE in more general flat-space gravities and excitations.

Abstract

We introduce a prescription to compute the entanglement entropy of Galilean conformal field theories by combining gravitational anomalies and an İnönü-Wigner contraction. We find that our expression for the entanglement entropy in the thermal limit reproduces the Cardy formula for Galilean conformal field theories. Using this proposal, we calculate the entanglement entropy for a class of Galilean conformal field theories, which are believed to be dual to three-dimensional flat-space cosmological solutions. These geometries describe expanding (contracting) universes and can be viewed as the flat-space limit of rotating Bañados-Teitelboim-Zanelli black holes. We show that our finding reduces, in the appropriate limits, to the results discussed in the literature and provide interpretations for the previously unexplored regimes, such as flat-space chiral gravity.