Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-06-17
Phys.Lett. B292 (1992) 283-289
Physics
High Energy Physics
High Energy Physics - Theory
(Plain Tex, 11pp, 4 figures available on request) SHEP 91/92-21
Scientific paper
10.1016/0370-2693(92)91176-A
We study further the r\^ole of the boundary operator $\O_B$ for macroscopic loop length in the stable definition of 2D quantum gravity provided by the $[{\tilde P},Q]=Q$ formulation. The KdV flows are supplemented by an additional flow with respect to the boundary cosmological constant $\sigma$. We numerically study these flows for the $m=1$, $2$ and $3$ models, solving for the string susceptibility in the presence of $\O_B$ for arbitrary coupling $\sigma$. The spectrum of the Hamiltonian of the loop quantum mechanics is continuous and bounded from below by $\sigma$. For large positive $\sigma$, the theory is dominated by the `universal' $m=0$ topological phase present only in the $[{\tilde P},Q]=Q$ formulation. For large negative $\sigma$, the non--perturbative physics approaches that of the $[P,Q]=1$ definition, although there is no path to the unstable solutions of the $[P,Q]=1$ $m$-even models.
Johnson Clifford V.
Morris Tim R.
White Peter L.
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