Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The moduli of annuli in random conformal geometry   We obtain exact formulae for three basic quantities in random conformal
geometry that depend on the modulus of an annulus. The first is for the law of
the modulus of the Brownian annulus describing the scaling limit of uniformly
sampled planar maps with annular topology, which is as predicted from the ghost
partition function in bosonic string theory. The second is for the law of the
modulus of the annulus bounded by a loop of a simple conformal loop ensemble
(CLE) on a disk and the disk boundary. The formula is as conjectured from the
partition function of the O$(n)$ loop model on the annulus derived by Cardy
(2006). The third is for the annulus partition function of the SLE$_{8/3}$ loop
introduced by Werner (2008). It again confirms a prediction of Cardy (2006).
The physics principle underlying our proofs is that 2D quantum gravity coupled
with conformal matters can be decomposed into three conformal field theories
(CFT): the matter CFT, the Liouville CFT, and the ghost CFT. At the technical
level, we rely on two types of integrability in Liouville quantum gravity, one
from the scaling limit of random planar maps, the other from the Liouville CFT.
We expect our method to be applicable to a variety of questions related to the
random moduli of non-simply-connected random surfaces.

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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th