On the Uniqueness of the Twisted Representation in the Z_2 Orbifold Construction of a Conformal Field Theory from a Lattice

Abstract

Following on from recent work describing the representation content of a meromorphic bosonic conformal field theory in terms of a certain state inside the theory corresponding to a fixed state in the representation, and using work of Zhu on a correspondence between the representations of the conformal field theory and representations of a particular associative algebra constructed from it, we construct a general solution for the state defining the representation and identify the further restrictions on it necessary for it to correspond to a ground state in the representation space. We then use this general theory to analyze the representations of the Heisenberg algebra and its $Z_2$-projection. The conjectured uniqueness of the twisted representation is shown explicitly, and we extend our considerations to the reflection-twisted FKS construction of a conformal field theory from a lattice.

27 pages LaTeX. Typos corrected -- no major changes

References in corpus (8)

• Meromorphic c=24 Conformal Field Theories
• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• Conformal Field Theories, Representations and Lattice Constructions
• Orbifold Constructions and the Classification of Self-Dual c=24 Conformal Field Theories
• Classification of Ten-Dimensional Heterotic Strings
• Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices
• Discussion of Self-Dual c=24 Conformal Field Theories
• Twisted representations of vertex operator algebras

Cited by in corpus (3)

• On Zhu's Associative Algebra as a Tool in the Representation Theory of Vertex Operator Algebras
• Intertwiners in Orbifold Conformal Field Theories
• Conjectured Z_2-Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 - the Neighborhood Graph