Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories

TL;DR

The work develops a Wilson-line holographic framework to compute entanglement entropy in 2D Galilean conformal field theories and extends it to flat space gravity in 2+1 dimensions. It systematically constructs flat-space holography via ISL$(2, ext{R})$ Chern-Simons theory, providing explicit EE formulas for zero and finite temperature GCFTs and for flat-space cosmologies (FSCs) with spin-2 and spin-3 charges. The results are cross-validated with GCFT calculations through the BMS/GCA correspondence, and extended to higher-spin flat-space gravity, offering a consistent non-AdS holographic dictionary. The approach yields concrete, testable predictions for entanglement and thermal entropy in flat space holography and sets the stage for further explorations in non-AdS holography and GCFT extensions.

Abstract

In this paper we will present in more detail a construction using Wilson lines and the corresponding dual Galilean conformal field theory calculations for analytically determining holographic entanglement entropy for flat space in $2+1$ dimensions first presented in hep-th/1410.4089. In addition we will show how the construction using Wilson lines can be expanded to flat space higher-spin theories and determine the thermal entropy of (spin-3 charged) flat space cosmologies using this approach.

Figures (2)

• Figure 1: Boosted ($A$, $B$) and equal time ($A'$, $B'$) entangled intervals used to determine entanglement entropy in GCFTs.
• Figure 2: Boosted ($A$, $B$) and equal time ($A'$, $B'$) entangled intervals and the correpsonding Wilson line ($\gamma_A$) used to determine holographic entanglement entropy in flat space.