2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53474\small 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 field theory of Liouville. 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.9High Energy Physics - Theorytext