Gravity in 2+1 dimensions as a Riemann-Hilbert problem

Details Gravity in 2+1 dimensions as a Riemann-Hilbert problem Gravity in 2+1 dimensions as a Riemann-Hilbert problem

1995-10-10

arxiv.org/abs/hep-th/9510060v1

Class.Quant.Grav. 13 (1996) 653-680

Physics

High Energy Physics

High Energy Physics - Theory

32 pages Latex, 4 figures (uuencoded)

Scientific paper

10.1088/0264-9381/13/4/007

In this paper we consider 2+1-dimensional gravity coupled to N point-particles. We introduce a gauge in which the $z$- and $\bar{z}$-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: $e^a_z(z)$ is equivalent to solving the Riemann-Hilbert problem for the group $SO(2,1)$. 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.

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