Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: New bounds for the free energy of directed polymers in dimension 1+1 and
  1+2
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph