Relating c<0 and c>0 Conformal Field Theories

TL;DR

This paper establishes a canonical mapping between certain negative and positive central charge conformal field theories, revealing shared state spaces and hidden symmetries, with implications for understanding their structural relationships.

Contribution

It introduces a novel canonical mapping linking c<0 ghost systems to c>0 scalar and Dirac theories, uncovering shared state spaces and hidden symmetries.

Findings

Shared state spaces between c<0 and c>0 theories.

Existence of hidden nonlocal sl(2) symmetries.

Mappings are suggested by character identities.

Abstract

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 nonlocal sl(2) symmetries.