Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The dimer model on Riemann surfaces, I   We develop a framework to study the dimer model on Temperleyan graphs
embedded on a Riemann surface with finitely many holes and handles. We extend
Temperley's bijection to this setting and show that the dimer model can be
understood in terms of an object which we call Temperleyan forests. Extending
our earlier work to the setup of Riemann surfaces, we show that if the
Temperleyan forest has a scaling limit then the fluctuations of the height
one-form of the dimer model also converge.
  Furthermore, if the Riemann surface is either a torus or an annulus, we show
that Temperleyan forests reduce to cycle-rooted spanning forests and show
convergence of the latter to a conformally invariant, universal scaling limit.
This generalises a result of Kassel--Kenyon. As a consequence, the dimer height
one-form fluctuations also converge on these surfaces, and the limit is
conformally invariant. Combining our results with those of Dub\'edat, this
implies that the height one-form on the torus converges to the compactified
Gaussian free field, thereby settling a question in \cite{DubedatGheissari}.
This is the first part in a series of works on the scaling limit of the dimer
model on general Riemann surfaces.

35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org