Modular origin of chiral diffeomorphisms and their fuzzy analogs in higher-dimensional quantum field theories

Abstract

The infinite-dimensional conformal symmetries beyond the Moebius-group (the vacuum symmetry) of chiral theories are shown to allow a natural derivation and interpretation in the operator-algebraic modular setting of algebraic QFT. In this way one learns that the diffeomorphisms of the circle beyond the Moebius group are bona fide Wigner symmetries with respect to suitably chosen non-vacuum state vector. The separation of chiral diffeomorphism symmetry from the issue of the structure of the energy–momentum tensor of 2-dimensional conformal theories permits the use of these symmetries in more general chiral theories which one encounters in the algebraic lightfront holography of massive d⩾1+1 dimensional QFTs. They only act locally on the lightfront projection but correspond to a new class of “fuzzy” symmetries in the original theory before the projection. These fuzzy symmetries remained hidden to quantization methods since they have a pure quantum origin; they do not require any spacetime noncommutativity and are in complete harmony with the causality and locality of the real time (non-commutative) operator algebra structure. Their use makes recent attempts to explain the desired universal structure of a possible future quantum Bekenstein-like area law in terms of Virasoro algebra structures on black hole horizons more palatable.