Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-point functions in c <= 1 Liouville theory and conformal loop
  ensembles   The possibility of extending the Liouville Conformal Field Theory from values
of the central charge $c \geq 25$ to $c \leq 1$ has been debated for many years
in condensed matter physics as well as in string theory. It was only recently
proven that such an extension -- involving a real spectrum of critical
exponents as well as an analytic continuation of the DOZZ formula for
three-point couplings -- does give rise to a consistent theory. We show in this
Letter that this theory can be interpreted in terms of microscopic loop models.
We introduce in particular a family of geometrical operators, and, using an
efficient algorithm to compute three-point functions from the lattice, we show
that their operator algebra corresponds exactly to that of vertex operators
$V_{\hat{\alpha}}$ in $c \leq 1$ Liouville. We interpret geometrically the
limit $\hat{\alpha} \to 0$ of $V_{\hat{\alpha}}$ and explain why it is not the
identity operator (despite having conformal weight $\Delta=0$).

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an