Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models
arXiv:0802.4298 · doi:10.1088/1751-8113/41/38/385201
Abstract
We reinterpret a path describing a state in an irreducible module of the unitary minimal model M(k+1,k+2) in terms of a string of charged operators acting on the module's ground-state path. Each such operator acts non-locally on a path. The path characteristics are then translated into a set of conditions on sequences of operators that provide an operator basis. As an application, we re-derive the vacuum finite fermionic character by constructing the generating function of these basis states. These results generalize directly to the M(k+1,2k+3) models, the close relatives of the unitary models in terms of path description.
22 pages, new title and abstract; section 1 rewritten and section 2.2 improved; version to appear in J. Phys. A