Entanglement entropy in Galilean conformal field theories and flat holography

TL;DR

This work derives an exact entanglement entropy formula for two-dimensional Galilean conformal field theories (GCFTs) and provides robust holographic checks in flat space via both geodesic and Chern-Simons/Wilson-line methods. By taking a nonrelativistic limit of the 2d CFT replica trick, the authors obtain EE for GCFTs as $S^{\text{GCFT}_2}_{\text{EE}} = \frac{c_L}{6}\ln(\ell_x/a) + \frac{c_M}{6}(\ell_y/\ell_x)$, with finite-temperature and finite-size generalizations. They then establish holographic EE for GCFTs in 3d flat spacetimes, showing consistency between field-theory results and holographic computations: EE expressions for null orbifold and flat space match the GCFT predictions and depend on the central charges $c_L$ and $c_M$ (with $c_M=3/G_N$ in Einstein gravity). The Chern-Simons formulation provides a complementary Wilson-line derivation that reproduces the same results, reinforcing the flat-space holography program and enabling extensions to higher dimensions and non-Einstein theories.

Abstract

We present the analytical calculation of entanglement entropy for a class of two dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography.