The Boundary Cosmological Constant in Stable 2D Quantum Gravity

Abstract

We study further the rôle of the boundary operator ${Ø}_B$ 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 ${Ø}_B$ 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.

(Plain Tex, 11pp, 4 figures available on request) SHEP 91/92-21

References in corpus (1)

• On Loop Equations In KdV Exactly Solvable String Theory

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