Codimension-two holography for wedges

Building tensor networks for holographic states

“…where |w c , γ (−) T T is a state defined by the lower-half Euclidean path-integral in the T T deformed theory, with the background metric γ (−) (w c ) and the T T coupling λ = 2πG N w 2 c . 8 One important detail which we must address here is that in order to prevent UV divergences 6 Our setup is also similar to that of wedge holography [73], but with wedge in Euclidean time τ instead of position x.…”

“…A concern here is that this regulator introduces a kink in the field theory path integral at u = u 0 ; this can be avoided by choosing a smooth boundary slice (i.e., with the kink at u 0 smoothed out). Alternatively, we could add the Hayward term at the corner, as was done in [73], but we expect these choices to only affect the very UV details of the entanglement structure of the state. 9 The states |w c , γ (−) T T were discussed recently in [41] in the context of Hartle-Hawking wavefunctions in the bulk, where they were called "metric eigenstates".…”

“…In what follows, we will be interested in an effective theory described by the region of the bulk geometry confined to the wedge between −θ c ≤ θ ≤ θ c . See similar computations in the context of recently-proposed wedge holography [73]. Since we will be interested in the region of space-time up to z = , coordinate u will be restricted to…”

Defect extremal surface as the holographic counterpart of Island formula

“…One can find the effective Newton constant on the brane by doing a Randall-Sundrum reduction along the extra dimension. In our case the Randall-Sundrum reduction is taken along ρ direction for wedge W 1 [71], then the 2d gravity theory on Q comes from the reduction of the 3d bulk. Together with the brane matter on Q, we get the full 2d brane theory to be a gravity theory plus CFT on the brane.…”

Chern-Simons gravity dual of BCFT

“…This leads to the structure so called the Island [31][32][33], which has been successfully applied to studies of black hole information [34][35][36][37][38]. Moreover, limits of AdS/BCFT lead to a series of codimension two holography [37,39,40] (see also [41]).…”