VACUUM INSTABILITY IN CHERN-SIMONS THEORY, NULL VECTORS AND 2-DIMENSIONAL LOGARITHMIC OPERATORS

A new relation between two-dimensional conformal field theories and th ree-dimensional topologically massive gauge theories is found, where t he dynamical nature of the 3d theory is ultimately important. It is sh own that the those primary states in CFT which have non-unitary descen dants correspond in the 3d theory to supercritical charges and cause v acuum instability. It is also shown that logarithmic operators separat ing the unitary sector from a non-unitary one correspond to an exact z ero energy ground state in which case the 3d Hamiltonian naturally has a Jordan structure. (C) 1998 Elsevier Science B.V. All rights reserve d.