2D Black Holes and 2D Gravity

Abstract

The SL(2, R)/U(1) coset model, with U(1) an element of the third conjugacy class of SL(2, R) subgroups, is considered. The resulting theory is seen to collapse to a one dimensional Liouville field theory. Then the 2 dimensional black hole SL(2, R)/U(1), with U(1) a non-compact subgroup boosted by a Lorentz transformation, is considered. In the limit of high boost, the resulting black hole is found to tend to the Liouville field coupled to a C = 1 matter field. The limit of the vertex operators of the 2 dimensional black hole also tend to those of the C = 1 two dimensional gravity.