Moretti, Valter and Pinamonti, Nicola (2003) Holography, SL(2,R) symmetry, Virasoro algebra and all that in Rindler spacetime. UNSPECIFIED. (Unpublished)
It is shown that it is possible to define quantum field theory of a massless scalar free field on the event horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys diffeomorfism invariance and turns out to be unitarily and algebraically equivalent to the analogous theory of a scalar field prapogating inside Rindler spacetime, nomatter the value of the mass of the field in the bulk. More precisely, there exist a unique transformation that realizes the bulk-boundary correspondence upon an appropriate choice for Fock representation spaces. Secondly, the found correspondence is a subcase of an analogous algebraic correspondence described by the injective homomorphisms of the abstract algebras of observables generated by abstract quantum free-field operators. These field operators are smeared with suitable test functions in the bulk and exact 1-forms on the horizon. In this sense the correspondence is independent from the chosen vacua. It is proven that, under that correspondence the 'hidden' SL(2,R) quantum symmetry found in a previous work gets a clear geometric meaning, it being associated with a group of diffeomorphisms of the horizon itself. Finally it is found that there is a possible enlargement of the quantum symmetry on the horizon to a quantum Virasoro symmetry associated with vector fields on the event horizon.
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