Punctured Haag Duality in Locally Covariant Quantum Field Theories

We investigate a new property of nets of local algebras over 4-dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point p of the spacetime. Punctured Haag duality implies Haag duality and local definiteness. Our main result is that, if we deal with a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, then also the converse holds. The free Klein-Gordon field provides an example in which this property is verified.