Abstract
Recently Leutheusser and Liu [1, 2] identified an emergent algebra of Type III1 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 III1 algebra becomes an algebra of Type II∞. The Type II∞ algebra is the crossed product of the Type III1 algebra by its modular automorphism group. In the context of the emergent Type II∞ 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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Witten, E. Gravity and the crossed product. J. High Energ. Phys. 2022, 8 (2022). https://doi.org/10.1007/JHEP10(2022)008
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DOI: https://doi.org/10.1007/JHEP10(2022)008