Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Running couplings with a vanishing scale anomaly   Running couplings can be understood as arising from the spontaneous breaking
of an exact scale invariance in appropriate effective theories with no
dilatation anomaly. Any ordinary quantum field theory, even if it has massive
fields, can be embedded into a theory with spontaneously broken exact scale
invariance in such a way that the ordinary running is recovered in the
appropriate limit, as long as the potential has a flat direction. These
scale-invariant theories, however, do not necessarily solve the cosmological
constant or naturalness problems, which become manifest in the need to
fine-tune dimensionless parameters.

1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ