Motivated by constructions in Algebraic Quantum Field Theory we introduce wedge domains in compac... more Motivated by constructions in Algebraic Quantum Field Theory we introduce wedge domains in compactly causal symmetric spaces $M=G/H$, which includes in particular anti-de Sitter space in all dimensions and its coverings. Our wedge domains generalize Rindler wedges in Minkowski space. The key geometric structure we use is the modular flow on $M$ defined by an Euler element in the Lie algebra of $G$. Our main geometric result asserts that three seemingly different characterizations of these domains coincide: the positivity domain of the modular vector field, the domain specified by a KMS-like analytic extension condition for the modular flow, and the domain specified by a polar decomposition in terms of certain cones. In the second half of the article we show that our wedge domains share important properties with wedge domains in Minkowski space. If $G$ is semisimple, there exist unitary representations $(U,{\mathcal {H}})$ of $G$ and isotone covariant nets of real subspaces $\textsf ...
Motivated by constructions in Algebraic Quantum Field Theory we introduce wedge domains in compac... more Motivated by constructions in Algebraic Quantum Field Theory we introduce wedge domains in compactly causal symmetric spaces $M=G/H$, which includes in particular anti-de Sitter space in all dimensions and its coverings. Our wedge domains generalize Rindler wedges in Minkowski space. The key geometric structure we use is the modular flow on $M$ defined by an Euler element in the Lie algebra of $G$. Our main geometric result asserts that three seemingly different characterizations of these domains coincide: the positivity domain of the modular vector field, the domain specified by a KMS-like analytic extension condition for the modular flow, and the domain specified by a polar decomposition in terms of certain cones. In the second half of the article we show that our wedge domains share important properties with wedge domains in Minkowski space. If $G$ is semisimple, there exist unitary representations $(U,{\mathcal {H}})$ of $G$ and isotone covariant nets of real subspaces $\textsf ...
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