Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-03-12
Nucl.Phys. B638 (2002) 351-377
Physics
High Energy Physics
High Energy Physics - Theory
32 pages LaTex
Scientific paper
We prove a relation between the asymptotic behavior of the conformal factor and the accessory parameters of the SU(1,1) Riemann- Hilbert problem. Such a relation shows the hamiltonian nature of the dynamics of N particles coupled to 2+1 dimensional gravity. A generalization of such a result is used to prove a connection between the regularized Liouville action and the accessory parameters in presence of general elliptic singularities. This relation had been conjectured by Polyakov in connection with 2-dimensional quantum gravity. An alternative proof, which works also in presence of parabolic singularities, is given by rewriting the regularized Liouville action in term of a background field.
Cantini Luigi
Menotti Pietro
Seminara Domenico
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