3D Flat Holography: Entropy and Logarithmic Corrections

TL;DR

This work analyzes the leading quantum corrections to the entropy of Flat Space Cosmologies (FSC) in 3D via a dual 2D Galilean Conformal Field Theory (GCFT), exploiting contracted modular invariance to derive a Cardy-like state-counting formula. It uncovers a universal logarithmic correction with coefficient $-\tfrac{3}{2}$, consistent with general thermodynamic fluctuation arguments and with the inner-horizon analysis of BTZ black holes in the AdS$_3$ limit. The authors connect bulk FSC thermodynamics to GCFT data, show how FSC arises as a flat-space limit of BTZ quotients, and extend the analysis to Topologically Massive Gravity where the leading term receives an extra contribution but the log correction remains unchanged. The results bolster flat-space holography in three dimensions and point to a rich mathematical structure, including a possible Jacobi-form-like behavior of GCFT partition functions that may illuminate the microscopic origin of the state counting.

Abstract

We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS3. The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes.