Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-11-09
Int. J. Mod. Phys. A10 (1995) 785-800
Physics
High Energy Physics
High Energy Physics - Theory
preprint ITEP-67-1993,16 p.,Latex file
Scientific paper
We describe the Hamiltonian reduction of the coajoint Kac-Moody orbits to the Virasoro coajoint orbits explicitly in terms of the Lagrangian approach for the Wess-Zumino-Novikov-Witten theory. While a relation of the coajoint Virasoro orbit $Diff \; S^1 /SL(2,R)$ to the Liouville theory has been already studied we analyse the role of special coajoint Virasoro orbits $Diff \; S^1/\tilde{T}_{\pm ,n}$ corresponding to stabilizers generated by the vector fields with double zeros. The orbits with stabilizers with single zeros do not appear in the model. We find an interpretation of zeros $x_i$ of the vector field of stabilizer $\tilde{T}_{\pm ,n}$ and additional parameters $q_i$, $i = 1,...,n$, in terms of quantum mechanics for $n$ point particles on the circle. We argue that the special orbits are generated by insertions of "wrong sign" Liouville exponential into the path integral. The additional parmeters $q_i$ are naturally interpreted as accessory parameters for the uniformization map. Summing up the contributions of the special Virasoro orbits we get the integrable sinh-Gordon type theory.
Gorsky Alexander
Johansen Anders
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