Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chiral Perturbation Theory Analysis of the Quark Condensate in a
  Magnetic Field   We present two-loop results for the quark condensate in an external magnetic
field within chiral perturbation theory using coordinate space techniques. At
finite temperature, we explore the impact of the magnetic field on the
pion-pion interaction in the quark condensate for arbitrary pion masses and
derive the correct weak magnetic field expansion in the chiral limit. At zero
temperature, we provide the complete two-loop representation for the vacuum
energy density and the quark condensate.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int