Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformal Symmetry and Differential Regularization of the Three-Gluon
  Vertex   The conformal symmetry of the QCD Lagrangian for massless quarks is broken
both by renormalization effects and the gauge fixing procedure. Renormalized
primitive divergent amplitudes have the property that their form away from the
overall coincident point singularity is fully determined by the bare
Lagrangian, and scale dependence is restricted to $\delta$-functions at the
singularity. If gauge fixing could be ignored, one would expect these
amplitudes to be conformal invariant for non-coincident points. We find that
the one-loop three-gluon vertex function $\Gamma_{\mu\nu\rho}(x,y,z)$ is
conformal invariant in this sense, if calculated in the background field
formalism using the Feynman gauge for internal gluons. It is not yet clear why
the expected breaking due to gauge fixing is absent. The conformal property
implies that the gluon, ghost and quark loop contributions to
$\Gamma_{\mu\nu\rho}$ are each purely numerical combinations of two universal
conformal tensors $D_{\mu\nu\rho}(x,y,z)$ and $C_{\mu\nu\rho}(x,y,z)$ whose
explicit form is given in the text. Only $D_{\mu\nu\rho}$ has an ultraviolet
divergence, although $C_{\mu\nu\rho}$ requires a careful definition to resolve
the expected ambiguity of a formally linearly divergent quantity.
Regularization is straightforward and leads to a renormalized vertex function
which satisfies the required Ward identity, and from which the beta-function is
easily obtained. Exact conformal invariance is broken in higher-loop orders,
but we outline a speculative scenario in which the perturbative structure of
the vertex function is determined from a conformal invariant primitive core by
interplay of the renormalization group equation and Ward identities.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol