Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Undecidable problems in quantum field theory   In the hope of providing some intellectual entertainment on April Fools' day
of this dark year, we point out that some questions in quantum field theory are
undecidable in a precise mathematical sense. More concretely, it will be
demonstrated that there is no algorithm answering whether a given 2d
supersymmetric Lagrangian theory breaks supersymmetry or not. It will also be
shown that there is a specific 2d supersymmetric Lagrangian theory which breaks
supersymmetry if and only if the standard Zermelo-Fraenkel set theory with the
axiom of choice is consistent, which can never be proved or disproved as the
consequence of G\"odel's second incompleteness theorem. The article includes a
brief and informal introduction to the phenomenon of undecidability and its
previous appearances in theoretical physics.

6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math