The Flat-Space Limit of AdS Coupled to a Bath

Abstract: We explain how to take a well-defined flat-space limit of brane models of AdS coupled to a non-gravitating bath. In the dual BCFT this amounts to a triple-scaling limit where both the number of boundary degrees of freedom and the boundary coupling are taken to infinity while the BCFT boundary piecewise approaches a lightcone. We show how this procedure acts on the conformal generators as a Wigner-.In\"on\"u contraction, reducing the global BCFT symmetry algebra to the global symmetry algebra of flat space. We discuss two natural notions of entanglement entropy of the flat-space dual. These are distinguished by whether modes that have left through $\mathcal I^\pm$ are included or not and give rise to a vanishing and non-trivial Page curve, respectively. Taking the flat-space limit of topological black holes we show that the Page time remains finite in two-dimensions. In $d > 2$ the Page time diverges in the flat limit, since AdS topological black holes become flat-space Rindler horizons.