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

P. S. Montague
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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.

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P. S. Montague. 1995-10-31. On the Uniqueness of the Twisted Representation in the Z_2 Orbifold Construction of a Conformal Field Theory from a Lattice. https://doi.org/10.1016/0550-3213(95)00486-c

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