Notes on Liouville Theory at c<=1 - High Energy Physics - TheoryReport as inadecuate

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Abstract: The continuation of the Liouville conformal field theory to c<=1 isconsidered. The viability of an interpretation involving a timelike boson whichis the conformal factor for two-dimensional asymptotically de Sitter geometriesis examined. The conformal bootstrap leads to a three-point function with aunique analytic factor which is the same as that which appears along with thefusion coefficients in the minimal models. A corresponding non-analytic factorproduces a well-defined metric on fields only when the central charge isrestricted to those of the topological minimal models, and when the conformaldimensions satisfy h>c-1-24. However, the theories considered here have acontinuous spectrum which excludes the degenerate representations appearing inthe minimal models. The c=1 theory has been investigated previously usingsimilar techniques, and is identical to a non-rational CFT which arises as alimit of unitary minimal models. When coupled to unitary matter fields, thenon-unitary theories with c<=-2 produce string amplitudes which are similar tothose of the minimal string.

Author: Will McElgin


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