Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $R^2$ 2D Quantum Gravity and Dually Weighted Graphs   A recently introduced model of dually weighted planar graphs is solved in
terms of an elliptic parametrization for some particular collection of planar
graphs describing the 2D $R^2$ quantum gravity. Along with the cosmological
constant $\lambda$ one has a coupling $\beta$ in the model corresponding to the
$R^2$-coupling constant. It is shown that for any value of $\beta$ the large
scale behavior of the model corresponds to that of the standard pure 2D quantum
gravity. On small distances it describes the dynamics of point-like curvature
defects introduced into the flat 2D space. The scaling function in the vicinity
of almost flat metric is obtained. The major steps of the exact solution are
given.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn