Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: QCD with Large Number of Quarks: Effects of the Instanton --
  Anti-instanton Pairs   We calculate the contribution of the instanton -- anti-instanton ($I\bar I$)
pairs to the vacuum energy of QCD-like theories with $N_f$ light fermions using
the saddle point method. We find a qualitative change of the behavior: for $N_f
\ge 6$ it starts to oscillate with $N_f$. Similar behaviour was known for
quantum mechanical systems interacting with fermions. We discuss the possible
consequences of this phenomenon, and its relation to the mechanism of chiral
symmetry breaking in these theories. We also discuss the asymptotics of the
perturbative series associated with the $I\bar I$ contribution, comparing our
results with those in literature.

16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph