805 research outputs found
Boundary Correlators in 2D Quantum Gravity: Liouville versus Discrete Approach
We calculate a class of two-point boundary correlators in 2D quantum gravity
using its microscopic realization as loop gas on a random surface. We find a
perfect agreement with the two-point boundary correlation function in Liouville
theory, obtained by V. Fateev, A. Zamolodchikov and Al. Zamolodchikov. We also
give a geometrical meaning of the functional equation satisfied by this
two-point function.Comment: 21 pages, 5 figures, harvmac, eqs. (2.11) and (5.11) correcte
Exact Solution of the Six-Vertex Model on a Random Lattice
We solve exactly the 6-vertex model on a dynamical random lattice, using its
representation as a large N matrix model. The model describes a gas of dense
nonintersecting oriented loops coupled to the local curvature defects on the
lattice. The model can be mapped to the c=1 string theory, compactified at some
length depending on the vertex coupling. We give explicit expression for the
disk amplitude and evaluate the fractal dimension of its boundary, the average
number of loops and the dimensions of the vortex operators, which vary
continuously with the vertex coupling.Comment: typos corrected and a figure added in Appendix
Boundary Ground Ring in 2D String Theory
The 2D quantum gravity on a disc, or the non-critical theory of open strings,
is known to exhibit an integrable structure, the boundary ground ring, which
determines completely the boundary correlation functions. Inspired by the
recent progress in boundary Liouville theory, we extend the ground ring
relations to the case of non-vanishing boundary Liouville interaction known
also as FZZT brane in the context of the 2D string theory. The ring relations
yield an over-determined set of functional recurrence equations for the
boundary correlation functions. The ring action closes on an infinite array of
equally spaced FZZT branes for which we propose a matrix model realization. In
this matrix model the boundary ground ring is generated by a pair of complex
matrix fields.Comment: sect. 5 extended, appendix adde
- …