ar X iv : h ep - t h / 01 06 06 4 v 1 7 J un 2 00 1 The Fuzzy Analog of Chiral Diffeomorphisms in higher dimensional Quantum Field Theories ∗

Our observation that the chiral diffeomorphisms allow an interpretation as modular groups of local operator algebras in the sense of Tomita and Takesaki allows us to conclude that the higher dimensional generalizations are certain infinite dimensional groups which act in a “fuzzy” way on the operator algebras of local quantum physics. These actions do not require any spacetime noncommutativity and are in complete harmony with causality and localization principles. The use of an appropriately defined holomorphic isomorphism reprocesses these fuzzy actions into partially geometric actions on the holographic image and in this way tightens the relation with chiral structures and makes recent attempts to explain the required universal structure of a would be quantum Bekenstein law in terms of Virasoro algebra structures more palatable.