Relating \(c<0\) and \(c>0\) conformal field theories. (English) Zbl 0945.81058
Summary: A ‘canonical mapping’ is established between the \(c=-1\) system of bosonic ghosts and the \(c=2\) complex scalar theory and a similar mapping between the \(c=-2\) system of fermionic ghosts and the \(c=1\) Dirac theory. The existence of this mapping is suggested by the identity of the characters of the respective theories. The respective \(c<0\) and \(c>0\) theories share the same space of states, whereas the spaces of conformal fields are different. Upon this mapping from their \(c<0\) counterparts, the \((c>0)\) complex scalar and the Dirac theories inherit hidden non-local \(sl(2)\) symmetries.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
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