THE BOUNDARY COSMOLOGICAL CONSTANT IN STABLE 2D QUANTUM-GRAVITY

We study further the role of the boundary operator O(B) for macroscopic loop length in the stable definition of 2D quantum gravitY Provided by the [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 [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.