Notes on Liouville Theory at c<=1

Details Notes on Liouville Theory at c<=1 Notes on Liouville Theory at c<=1

2007-06-04

arxiv.org/abs/0706.0365v1

Phys.Rev.D77:066009,2008

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 4 figures

Scientific paper

10.1103/PhysRevD.77.066009

The continuation of the Liouville conformal field theory to c<=1 is considered. The viability of an interpretation involving a timelike boson which is the conformal factor for two-dimensional asymptotically de Sitter geometries is examined. The conformal bootstrap leads to a three-point function with a unique analytic factor which is the same as that which appears along with the fusion coefficients in the minimal models. A corresponding non-analytic factor produces a well-defined metric on fields only when the central charge is restricted to those of the topological minimal models, and when the conformal dimensions satisfy h>(c-1)/24. However, the theories considered here have a continuous spectrum which excludes the degenerate representations appearing in the minimal models. The c=1 theory has been investigated previously using similar techniques, and is identical to a non-rational CFT which arises as a limit of unitary minimal models. When coupled to unitary matter fields, the non-unitary theories with c<=-2 produce string amplitudes which are similar to those of the minimal string.

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