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Gravity and the Crossed Product
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Gravity and the Crossed Product
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Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type III$_1$ in the operator algebra of ${\mathcal N}=4$ super Yang-Mills theory for large $N$. Here we describe some $1/N$ corrections to this picture and show that the emergent Type III$_1$ algebra becomes an algebra of Type II$_\infty$. The Type II$_\infty$ algebra is the crossed product of the Type III$_1$ algebra by its modular automorphism group. In the context of the emergent Type II$_\infty$ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.
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Cited by 28 Pith papers
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Albertian Channel Memory in Black-Hole Evaporation
An Albert algebra description of the horizon yields a Volterra memory law on the Reissner-Nordstrom evaporation trajectory whose spectral overlap reconstructs the Page curve envelope without restoring standard AMPS te...
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