Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On emergence in gauge theories at the 't Hooft limit   The aim of this paper is to contribute to a better conceptual understanding
of gauge quantum field theories, such as quantum chromodynamics, by discussing
a famous physical limit, the 't Hooft limit, in which the theory concerned
often simplifies.
  The idea of the limit is that the number $N$ of colours (or charges) goes to
infinity. The simplifications that can happen in this limit, and that we will
consider, are: (i) the theory's Feynman diagrams can be drawn on a plane
without lines intersecting (called `planarity'); and (ii) the theory, or a
sector of it, becomes integrable, and indeed corresponds to a well-studied
system, viz. a spin chain. Planarity is important because it shows how a
quantum field theory can exhibit extended, in particular string-like,
structures; in some cases, this gives a connection with string theory, and thus
with gravity.
  Previous philosophical literature about how one theory (or a sector, or
regime, of a theory) might be emergent from, and-or reduced to, another one has
tended to emphasize cases, such as occur in statistical mechanics, where the
system before the limit has finitely many degrees of freedom. But here, our
quantum field theories, including those on the way to the 't Hooft limit, will
have infinitely many degrees of freedom.
  Nevertheless, we will show how a recent schema by Butterfield and taxonomy by
Norton apply to the quantum field theories we consider; and we will classify
three physical properties of our theories in these terms. These properties are
planarity and integrability, as in (i) and (ii) above; and the behaviour of the
beta-function reflecting, for example, asymptotic freedom.
  Our discussion of these properties, especially the beta-function, will also
relate to recent philosophical debate about the propriety of assessing quantum
field theories, whose rigorous existence is not yet proven.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat