Gravity and the crossed product

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41 Scopus citations


Recently Leutheusser and Liu [1, 2] identified an emergent algebra of Type III1 in the operator algebra of 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.

Original languageEnglish (US)
Article number8
JournalJournal of High Energy Physics
Issue number10
StatePublished - Oct 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • 1/N Expansion
  • AdS-CFT Correspondence
  • Black Holes


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