Abstract
We argue that given holographic CFT1 in some state with a dual spacetime geometry M, and given some other holographic CFT2, we can find states of CFT2 whose dual geometries closely approximate arbitrarily large causal patches of M, provided that CFT1 and CFT2 can be non-trivially coupled at an interface. Our CFT2 states are “dressed up as” states of CFT1: they are obtained from the original CFT1 state by a regularized quench operator defined using a Euclidean path-integral with an interface between CFT2 and CFT1. Our results are consistent with the idea that the precise microscopic degrees of freedom and Hamiltonian of a holographic CFT are only important in fixing the asymptotic behavior of a dual spacetime, while the interior spacetime of a region spacelike separated from a boundary time slice is determined by more universal properties (such as entanglement structure) of the quantum state at this time slice. Our picture requires that low-energy gravitational theories related to CFTs that can be non-trivially coupled at an interface are part of the same non-perturbative theory of quantum gravity.
Highlights
We argue that given holographic CFT1 in some state with a dual spacetime geometry M, and given some other holographic CFT2, we can find states of CFT2 whose dual geometries closely approximate arbitrarily large causal patches of M, provided that CFT1 and CFT2 can be non-trivially coupled at an interface
Our results are consistent with the idea that the precise microscopic degrees of freedom and Hamiltonian of a holographic CFT are only important in fixing the asymptotic behavior of a dual spacetime, while the interior spacetime of a region spacelike separated from a boundary time slice is determined by more universal properties of the quantum state at this time slice
We follow the standard AdS/CFT recipe to understand the dual geometry to this state; the same type of geometries were considered recently in [11]; some of our technical results overlap with results in that paper, but we present the solutions for completeness
Summary
Given two different CFTs, we can define a single theory on some spacetime where the local degrees of freedom on half of the space are those of CFT1 and the local degrees of freedom of the other half of the space are those of CFT2. A useful way to think about an interface between two different CFTs is as a boundary condition for the CFT which is the tensor product between CFT1 and CFT2.8 Here, we are using the so-called “folding trick” [13], where the half-space on which CFT1 is defined is identified with the half-space on which CFT2 is defined. From this perspective, we can say that CFT1 and CFT2 are compatible if there is a boundary condition for the product theory that couples the two bulk theories non-trivially.. The allowed boundary conditions for the CF T1 ⊗ CF T2 tensor product CFT are constrained by crossing symmetry and unitarity, and might in principle be classified by a bootstrap approach (see e.g. [14])
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