Abstract
We use the isomorphism between the and the algebras to reconsider some generic aspects of conformal field theories (CFTs) with the algebra defined as a chiral symmetry. For unitarity theories, it is known that the extended symmetry generator acts trivially, and the resulting theory is equivalent to a CFT with a Virasoro symmetry only. For nonunitary CFTs, we define an operator depending on a nilpotent variable, and we organize the Verma module through the action of this new operator. Finally, we find the conditions imposed by the modified Ward identity.
- Received 29 April 2018
DOI:https://doi.org/10.1103/PhysRevD.98.026014
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Published by the American Physical Society