TY - JOUR
A2 - Kerner, Richard
AU - Todorov, Ivan
PY - 2010
DA - 2010/01/27
TI - Gauge Symmetry and Howe Duality in 4D Conformal Field Theory Models
SP - 509538
VL - 2010
AB - It is known that there are no local scalar Lie fields in more thantwo dimensions. Bilocal fields, however, which naturally arise in conformal operator product expansions, do generate infinite Lie algebras. It is demonstrated that these Lie algebras of local observables admit (highly reducible) unitary positive energy representations in a Fock space. Themultiplicity of their irreducible components is governed by a compact gauge group. The mutually commuting observable algebra and gauge group form a dual pair in the sense of Howe. In a theory of local scalar fields of conformal dimension two in four space-time dimensions the associated dual pairs are constructed and classified.
SN - 1687-9120
UR - https://doi.org/10.1155/2010/509538
DO - 10.1155/2010/509538
JF - Advances in Mathematical Physics
PB - Hindawi Publishing Corporation
KW -
ER -