Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Imaginary Geometry I: Interacting SLEs   Fix constants \chi >0 and \theta \in [0,2\pi), and let h be an instance of
the Gaussian free field on a planar domain. We study flow lines of the vector
field e^{i(h/\chi+\theta)} starting at a fixed boundary point of the domain.
Considering all \theta \in [0,2\pi), one obtains a family of curves that look
locally like SLE_\kappa, with \kappa \in (0,4), where \chi = 2/\kappa^{1/2} -
\kappa^{1/2}/2, which we interpret as the rays of a random geometry with purely
imaginary curvature.
  We extend the fundamental existence and uniqueness results about these paths
to the case that the paths intersect the boundary. We also show that flow lines
of different angles cross each other at most once but (in contrast to what
happens when h is smooth) may bounce off of each other after crossing. Flow
lines of the same angle started at different points merge into each other upon
intersecting, forming a tree structure. We construct so-called counterflow
lines (SLE_{16/\kappa}) within the same geometry using ordered "light cones" of
points accessible by angle-restricted trajectories and develop a robust theory
of flow and counterflow line interaction.
  The theory leads to new results about SLE. For example, we prove that
SLE_\kappa(\rho) processes are almost surely continuous random curves, even
when they intersect the boundary, and establish Duplantier duality for general
SLE_{16/\kappa}(\rho) processes.

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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph