We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a nonperturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find d H ≈ 3.8, in support of recent theoretical calculations that d H = 4. We also discuss the back-reaction of matter on the geometry.

Madras 600113 INDIAWe study c < 1 matter coupled to gravity in the Coulomb gas formalism using the double cohomology of the string BRST and Felder BRST charges. We find that states outside the primary conformal grid are related to the states of non-zero ghost number by means of descent equations given by the double cohomology. Some aspects of the Virasoro structure of the Liouville Fock space are studied. As a consequence, states of non-zero ghost number are easily constructed by "solving" these descent equations. This enables us to map ghost number conserving correlation functions involving non-zero ghost number states into those involving states outside the primary conformal grid.December 91 1

Madras 600 113, INDIAWe show how the double cohomology of the String and Felder BRST charges naturally leads to the ring structure of c < 1 strings. The chiral ring is a ring of polynomials in two variables modulo an equivalence relation of the form x p ≃ y p+1 for the (p+1, p) model.We also study the states corresponding to the edges of the conformal grid whose inclusion is crucial for the closure of the ring. We introduce candidate operators that correspond to the observables of the matrix models. Their existence is motivated by the relation of one of the screening operators of the minimal model to the zero momentum dilaton.

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Using a description of defects in solids in terms of three-dimensional gravity, we study the propagation of electrons in the background of disclinations and screw dislocations. We study the situations where there are bound states that are effectively localized on the defect and hence can be described in terms of an effective 1 + 1 dimensional field theory for the low energy excitations. In the case of screw dislocations, we find that these excitations are chiral and can be described by an effective field theory of chiral fermions. Fermions of both chirality occur even for a given direction of the magnetic field. The "net" chirality of the system however is not always the same for a given direction of the magnetic field, but changes from one sign of the chirality through zero to the other sign as the Fermi momentum or the magnitude of the magnetic flux 1 is varied. On coupling to an external electromagnetic field, the latter becomes anomalous, and predicts novel conduction properties for these materials.