Even lattices in an indefinite bilinear form classify two-dimensional conformal net extensions of Heisenberg nets under a discreteness assumption, with explicit rational and non-rational examples.
Chiral Observables and Modular Invariants
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abstract
Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general characteristics of modular invariant partition functions, although SL(2,Z) transformation properties are not assumed. First steps towards classification are made.
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Rational and non-rational two-dimensional conformal field theories arising from lattices
Even lattices in an indefinite bilinear form classify two-dimensional conformal net extensions of Heisenberg nets under a discreteness assumption, with explicit rational and non-rational examples.