A solvable low-energy effective theory based on the warped Virasoro group with three cocycles is constructed, and its one-loop-exact partition function and thermodynamics are derived.
Extensions of Virasoro group and Virasoro algebra by modules of tensor-densities on $S^1$
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abstract
We classify non-trivial (non-central) extensions of the group $Diff^+(S^1)$ of all diffeomorphisms of the circle preserving its orientation and of the Lie algebra $Vect (S^1)$ of vector fields on $S^1$, by the modules of tensor-densities on $S^1$. The result is: 4 non-trivial extensions of $Diff^+(S^1)$ and 7 non-trivial extensions of $Vect (S^1)$. Analogous results hold for the Virasoro group and the Virasoro algebra. We also classify central extensions of constructed Lie algebras. CPT-94/P.3024
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Warped Schwarzian theory
A solvable low-energy effective theory based on the warped Virasoro group with three cocycles is constructed, and its one-loop-exact partition function and thermodynamics are derived.