The FZZ-Duality Conjecture - A Proof

Details The FZZ-Duality Conjecture - A Proof The FZZ-Duality Conjecture - A Proof

2008-05-26

arxiv.org/abs/0805.3931v1

Physics

High Energy Physics

High Energy Physics - Theory

42 pages

Scientific paper

10.1088/1126-6708/2009/03/095

We prove that the cigar conformal field theory is dual to the Sine-Liouville model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov. Since both models possess the same chiral algebra, our task is to show that correlations of all tachyon vertex operators agree. We accomplish this goal through an off-critical version of the geometric Langlands duality for sl(2). More explicitly, we combine the well-known self-duality of Liouville theory with an intriguing correspondence between the cigar and Liouville field theory. The latter is derived through a path integral treatment. After a very detailed discussion of genus zero amplitudes, we extend the duality to arbitrary closed surfaces.

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