Abstract
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such quotients is developed using the Coulomb gas representation. Examples of parafermions, S U ( 2 ) current algebra and the N = 2 minimal models are described explicitly. The partition functions and the dimensions of the disordered fields are given. This result is a tool for finding new theories. For instance, it is of importance in analyzing the conformal field theories of exceptional holonomy manifolds.
Highlights
We consider here the quotient conformal field theory obtained by twisting with respect to this symmetry
From the point of view of conformal field theory (CFT), this quotient is quite complicated since every field in the Hilbert space transforms independently, and is not organized by some characters of an extended algebra
The following method to compute the partition function
Summary
We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. If not all, known rational conformal theories may be described by a system of free bosons moving on a Lorentzian lattice with a background charge. We derive the partition function of Cin the cases of Zk parafermions, SU (2)k current algebra and kth N = 2 minimal model, and leave to further work the consideration of other models. The results described here for N = 2 minimal models are of importance in the study of the conformal field theories of compactification of string theory on exceptional holonomy manifolds [5].
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