1,845 research outputs found
Spontaneous Breaking of Scale Invariance in a d=3 U(N) Model with Chern-Simons Gauge Field
We study spontaneous breaking of scale invariance in the large N limit of
three dimensional Chern-Simons theories coupled to a scalar field
in the fundamental representation. When a
self interaction term is added to the action we find a massive phase at a
certain critical value for a combination of the and 't Hooft's
couplings. This model attracted recent attention since at
finite it contains a singlet sector which is conjectured to be dual to
Vasiliev's higher spin gravity on . Our paper concentrates on the
massive phase of the 3d boundary theory. We discuss the advantage of
introducing masses in the boundary theory through spontaneous breaking of scale
invariance.Comment: 23 pages, 8 figures. several lines changed in the introduction. typos
correcte
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
Rectangular Layouts and Contact Graphs
Contact graphs of isothetic rectangles unify many concepts from applications
including VLSI and architectural design, computational geometry, and GIS.
Minimizing the area of their corresponding {\em rectangular layouts} is a key
problem. We study the area-optimization problem and show that it is NP-hard to
find a minimum-area rectangular layout of a given contact graph. We present
O(n)-time algorithms that construct -area rectangular layouts for
general contact graphs and -area rectangular layouts for trees.
(For trees, this is an -approximation algorithm.) We also present an
infinite family of graphs (rsp., trees) that require (rsp.,
) area.
We derive these results by presenting a new characterization of graphs that
admit rectangular layouts using the related concept of {\em rectangular duals}.
A corollary to our results relates the class of graphs that admit rectangular
layouts to {\em rectangle of influence drawings}.Comment: 28 pages, 13 figures, 55 references, 1 appendi
The Dirichlet space: A Survey
In this paper we survey many results on the Dirichlet space of analytic
functions. Our focus is more on the classical Dirichlet space on the disc and
not the potential generalizations to other domains or several variables.
Additionally, we focus mainly on certain function theoretic properties of the
Dirichlet space and omit covering the interesting connections between this
space and operator theory. The results discussed in this survey show what is
known about the Dirichlet space and compares it with the related results for
the Hardy space.Comment: 35 pages, typoes corrected, some open problems adde
Potential Theory on Trees, Graphs and Ahlfors Regular Metric Spaces
We investigate connections between potential theories on a Ahlfors-regular
metric space X, on a graph G associated with X, and on the tree T obtained by
removing the "horizontal edges" in G. Applications to the calculation of set
capacity are given.Comment: 45 pages; presentation improved based on referee comment
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