Defect extremal surface as the holographic counterpart of Island formula

Abstract

We propose defect extremal surface as the holographic counterpart of boundary quantum extremal surface. The defect extremal surface is defined by minimizing the Ryu-Takayanagi surface corrected by the defect theory. This is particularly interesting when the RT surface crosses or terminates on the defect. In a simple set up of AdS/BCFT, we find that the defect extremal surface formula gives precisely the same results of the boundary quantum extremal surface. We provide a decomposition procedure of an AdS bulk with a defect brane to see clearly how quantum extremal surface formula emerges from a brane world system with gravity glued to a flat space quantum field theory.

Phases of holographic interfaces

“…The Ryu-Takayanagi (RT) surfaces [58,59] are another natural class of curves whose intersection with the wall should be studied along lines similar to refs. [21,22] for BCFT.…”

“…3 It is clearly of interest to study if these surfaces intersect the domain wall, as is done for BCFT in refs. [21,22]. We hope to return to this question elsewhere.…”

“…When a holographic dual exists, Witten has argued that the appearance of a black hole at the Hawking-Page (HP) transition signals deconfinement in the gauge theory [90]. Assuming this interpretation 22 leads to the conclusion that in warm phases a confined theory coexists with a deconfined one. We will see below that such coexistence is easier when the confined theory is CFT 2 , i.e.…”

“…the theory with the larger central charge. 23 This is natural 22 There is an extensive literature on the subject including [91,92], studies specific to two dimensions [93,94], and recent discussions in relation with the superconformal index in N = 4 super Yang Mills [95][96][97][98]. For an introductory review see [99].…”

“…Such walls figure in models of localized gravity [2][3][4], in holographic duals of conformal interfaces [5][6][7], in efforts to embed inflation in string theory by studying dynamical bubbles [8][9][10][11], and more recently, following the ideas in refs. [12][13][14], in toy models of black hole evaporation [15][16][17][18][19][20][21][22][23]. Besides being a simple form of matter coupled to gravity, domain walls are also a key ingredient [24] in effective descriptions of the string-theory landscape -see [25][26][27] for some recent discussions of domain walls in this context.…”