BCFT and Islands in two dimensions

Abstract

By combining the AdS/BCFT correspondence and the brane world holography, we expect an equivalence relation between a boundary conformal field theory (BCFT) and a gravitational system coupled to a CFT. However, it still remains unclear how the boundary condition of the BCFT is translated in the gravitational system. We examine this duality relation in a two-dimensional setup by looking at the computation of entanglement entropy and energy flux conservation. We also identify the two-dimensional gravity which is dual to the boundary dynamics of a BCFT. Moreover, we show that by considering a gravity solution with scalar fields turned on, we can reproduce one point functions correctly in the AdS/BCFT.

The PEE aspects of entanglement islands from bit threads

“…Naturally, this third scenario is reminiscent of the double holographic model proposed in the recent studies of the black hole information problem [5], in which the von Neumann entropy of the Hawking radiation R can be computed by the island prescription (1.1). Interestingly, this connection can be more accurately clarified through the framework of braneworld holography [10][11][12][13].…”

“…That is, S (R) can be holographically calculated by the area of the minimal extremal surface in the dual geometry homologous to the boundary region R. The minimal extremal surface Γ R is called the RT surface in the AdS/BCFT setup, and I is a region on the Q brane, which is also named as entanglement island in the recent context [10][11][12][13], for reasons reviewed in the next subsection. The difference between the above formula and the traditional holographic RT formula is that, now the RT surface calculating the entanglement entropy of subregion R can not only be chosen as the connected extremal surface extended from the boundary of R (i.e., ∂R), but also the disconnected type, which can anchor on the Q brane.…”

“…The interesting holographic triality property of the AdS/BCFT correspondence has attracted a lot of attention in the context of the black hole information problem recently [10][11][12][13]. As shown in the figure 2, the upper picture shows the usual AdS/BCFT correspondence, that is, we can describe a d dimensional BCFT (which has a d − 1 dimensional boundary) equivalently using an Einstein gravity on an asymptotically AdS d+1 space containing an According to this, one can obtain a third equivalent picture, that is, a non-gravitational CFT d is glued to a gravitational theory on the AdS d space.…”

“…AdS/BCFT setup is actually equivalent [10][11][12][13]. 4 In particular, we have written the holographic entanglement entropy formula in a similar way as the island rule.…”

“…This formula instructs us that when calculating the finegrained entropy of a subregion R of the nongravitating region, one should carefully account for the contribution of degrees of freedom in a particular region of the gravitational part, a surprising region called island. Interestingly, the work of [10,11] (see also [5,12,13,64]) shows that, in fact the island formula (1.1) in the "black hole + radiation" setup is equivalent to the holographic entanglement entropy formula in the AdS/BCFT setup. This allows us to investigate various problems related to the concept of "island" in the black hole information problem in the simple AdS/BCFT setup.…”