Cutoff brane vs the Karch-Randall brane: the fluctuating case

A bstract Recently, certain holographic Weyl transformed CFT 2 is proposed to capture the main features of the AdS 3 /BCFT 2 correspondence [1, 2]. In this paper, by adapting the Weyl transformation, we simulate a generalized AdS/BCFT set-up where the fluctuation of the Karch-Randall (KR) brane is considered. In the gravity dual of the Weyl transformed CFT, the so-called cutoff brane induced by the Weyl transformation plays the same role as the KR brane. Unlike the non-fluctuating configuration, in the 2 d effective theory the additional twist operator is inserted at a different place, compared with the one inserted on the brane. Though this is well-understood in the Weyl transformed CFT set-up, it is confusing in the AdS/BCFT set-up where the effective theory is supposed to locate on the brane. This confusion indicates that the KR brane may be emergent from the boundary CFT 2 via the Weyl transformations. We also calculate the balanced partial entanglement (BPE) in the fluctuating brane configurations and find it coincide with the entanglement wedge cross-section (EWCS). This is a non-trivial test for the correspondence between the BPE and the EWCS, and a non-trivial consistency check for the Weyl transformed CFT set-up.