1 research outputs found
Gravity in 2+1 dimensions as a Riemann-Hilbert problem
In this paper we consider 2+1-dimensional gravity coupled to N
point-particles. We introduce a gauge in which the - and
-components of the dreibein field become holomorphic and
anti-holomorphic respectively. As a result we can restrict ourselves to the
complex plane. Next we show that solving the dreibein-field: is
equivalent to solving the Riemann-Hilbert problem for the group . We
give the explicit solution for 2 particles in terms of hypergeometric
functions. In the N-particle case we give a representation in terms of
conformal field theory. The dreibeins are expressed as correlators of 2 free
fermion fields and twistoperators at the position of the particles.Comment: 32 pages Latex, 4 figures (uuencoded