Deformed CFTs on a strip with a stretched-horizon conformal boundary are proposed as UV completions of pure and matter-coupled JT gravity, reproducing its entropy and a Page-curve-like saturation.
A Type $I$ Approximation of the Crossed Product
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I show that an analog of the crossed product construction that takes type $III_{1}$ algebras to type $II$ algebras exists also in the type $I$ case. This is particularly natural when the local algebra is a non-trivial direct sum of type $I$ factors. Concretely, I rewrite the usual type $I$ trace in a different way and renormalise it. This new renormalised trace stays well-defined even when each factor is taken to be type $III$. I am able to recover both type $II_{\infty}$ as well as type $II_{1}$ algebras by imposing different constraints on the central operator in the code. An example of this structure appears in holographic quantum error-correcting codes; the central operator is then the area operator.
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JT gravity and deformed CFTs
Deformed CFTs on a strip with a stretched-horizon conformal boundary are proposed as UV completions of pure and matter-coupled JT gravity, reproducing its entropy and a Page-curve-like saturation.