Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The local Callan-Symanzik equation: structure and applications   The local Callan-Symanzik equation describes the response of a quantum field
theory to local scale transformations in the presence of background sources.
The consistency conditions associated with this anomalous equation imply
non-trivial relations among the $\beta$-function, the anomalous dimensions of
composite operators and the short distance singularities of correlators. In
this paper we discuss various aspects of the local Callan-Symanzik equation and
present new results regarding the structure of its anomaly. We then use the
equation to systematically write the n-point correlators involving the trace of
the energy-momentum tensor. We use the latter result to give a fully detailed
proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also
correspond to CFTs. We also clarify the relation between the matrix entering
the gradient flow formula for the $\beta$-function and a manifestly positive
metric in coupling space associated with matrix elements of the trace of the
energy momentum tensor.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin