TOPOLOGICAL DEFECTS ON FLUCTUATING SURFACES - GENERAL-PROPERTIES AND THE KOSTERLITZ-THOULESS TRANSITION

We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine- Gordon Hamiltonian to describe it. The. Coulomb-gas Hamiltonian includ es charge densities arising from disclinations and from Gaussian curva ture. There is an interaction coupling the difference between these tw o densities, whose strength is determined by the hexatic rigidity, and an interaction coupling Gaussian curvature densities arising from the Liouville Hamiltonian resulting from the imposition of a covariant cu toff. In the sine-Gordon Hamiltonian, there is a Linear coupling betwe en a scalar field and the Gaussian curvature. We discuss a gauge-invar iant correlation function for hexatic order and the dielectric constan t of the Coulomb gas. We also derive renormalization-group recursion r elations that predict a transition with decreasing bending rigidity ka ppa.