Algebra of operators in an AdS-Rindler wedge

Article Physics, Particles & Fields

An algebra of observables for de Sitter space

Venkatesa Chandrasekaran et al.

Summary: We present an algebra of observables for a static patch in de Sitter space, where the operators are gravitationally dressed according to the observer's worldline. This algebra belongs to the Type II1 von Neumann algebra. The state of this algebra has a natural concept of entropy, with a maximum entropy state corresponding to empty de Sitter space. The entropy of any semiclassical state of the Type II1 algebras agrees, up to an arbitrary additive constant, with the expected generalized entropy S-gen = (A/4G(N)) + S-out.

JOURNAL OF HIGH ENERGY PHYSICS (2023)

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Article Physics, Particles & Fields

Gravity and the crossed product

Edward Witten

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.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

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Article Physics, Particles & Fields