Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator mixing in massless QCD-like theories and Poincare'-Dulac
  theorem   Recently, a geometric approach to operator mixing in massless QCD-like
theories -- that involves canonical forms based on the Poincare'-Dulac theorem
for the linear system that defines the renormalized mixing matrix in the
coordinate representation $Z(x,\mu)$ -- has been advocated in arXiv:2103.15527
. As a consequence, a classification of operator mixing in four cases --
depending on the canonical forms of $- \frac{\gamma(g)}{\beta(g)}$, with
$\gamma(g)=\gamma_0 g^2+\cdots$ the matrix of the anomalous dimensions and
$\beta(g)=-\beta_0 g^3 + \cdots$ the beta function -- has been proposed: (I)
nonresonant $\frac{\gamma_0}{\beta_0}$ diagonalizable, (II) resonant
$\frac{\gamma_0}{\beta_0}$ diagonalizable, (III) nonresonant
$\frac{\gamma_0}{\beta_0}$ nondiagonalizable, (IV) resonant
$\frac{\gamma_0}{\beta_0}$ nondiagonalizable. In particular, in
arXiv:2103.15527 a detailed analysis of the case (I) -- where operator mixing
reduces to all orders of perturbation theory to the multiplicatively
renormalizable case -- has been provided. In the present paper, following the
aforementioned approach, we work out in the remaining three cases the canonical
forms for $- \frac{\gamma(g)}{\beta(g)}$ to all orders of perturbation theory,
the corresponding UV asymptotics of $Z(x,\mu)$, and the physics interpretation.
We also work out in detail physical realizations of the cases (I) and (II).

32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex