Gravity and the crossed product

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 infinity. The Type II infinity algebra is the crossed product of the Type III1 algebra by its modular automorphism group. In the context of the emergent Type II infinity 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.

Automated summary

In this study, an emergent algebra in the operator algebra of N = 4 super Yang-Mills theory was identified. The 1/N corrections to this algebra led to the emergence of a Type II infinity algebra. In this context, the entropy of a black hole state is well-defined and independent of the state.