Vacuum Instability in Chern-Simons Theory, Null Vectors and Two-Dimensional Logarithmic Operators

Abstract

A new relation between two-dimensional conformal field theories and three-dimensional topologically massive gauge theories is found, where the dynamical nature of the 3d theory is ultimately important. It is shown that the those primary states in CFT which have non-unitary descendants correspond in the 3d theory to supercritical charges and cause vacuum instability. It is also shown that logarithmic operators separating the unitary sector from a non-unitary one correspond to an exact zero energy ground state in which case the 3d Hamiltonian naturally has a Jordan structure.

12 pages, Latex. 1 figure

References in corpus (1)

• Origin of Logarithmic Operators in Conformal Field Theories

Cited by in corpus (13)

• Operator Product Expansion in Logarithmic Conformal Field Theory
• Logarithmic conformal field theory approach to topologically massive gravity
• Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)
• Topologically massive gravity on AdS${}_2$ spacetimes
• Extended chiral algebras in the SU(2)_0 WZNW model
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• Vacuum Instability in Topologically Massive Gauge Theory
• Extended multiplet structure in Logarithmic Conformal Field Theories
• Critical gravity on AdS2 spacetimes
• Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory
• Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
• D-Branes in Topological Membranes