Relating c < 0 and c > 0 conformal field theories Original Research Article

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.