3,326 research outputs found
From rubber bands to rational maps: A research report
This research report outlines work, partially joint with Jeremy Kahn and
Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal
surfaces with boundary. One one hand, this lets us tell when one rubber band
network is looser than another, and on the other hand tell when one conformal
surface embeds in another.
We apply this to give a new characterization of hyperbolic critically finite
rational maps among branched self-coverings of the sphere, by a positive
criterion: a branched covering is equivalent to a hyperbolic rational map if
and only if there is an elastic graph with a particular "self-embedding"
property. This complements the earlier negative criterion of W. Thurston.Comment: 52 pages, numerous figures. v2: New example
TOPOLOGICAL MATTER, MIRROR SYMMETRY AND NON-CRITICAL (SUPER)STRINGS
We study the realization of the (super) conformal topological symmetry in
two-dimensional field theories. The mirror automorphism of the topological
algebra is represented as a reflection in the space of fields. As a
consequence, a double BRST structure for topological matter theories is found.
It is shown that the implementation of the topological symmetry in non-critical
(super)string theories depends on the matter content of the two realizations
connected by the mirror transformation.Comment: 45 pages, phyzzx, no figure
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
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