Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Platonic Field Theories   We study renormalization group (RG) fixed points of scalar field theories
endowed with the discrete symmetry groups of regular polytopes. We employ the
functional perturbative renormalization group (FPRG) approach and the
$\epsilon$-expansion in $d=d_c-\epsilon$. The upper critical dimensions
relevant to our analysis are $d_c =
6,4,\frac{10}{3},3,\frac{14}{5},\frac{8}{3},\frac{5}{2},\frac{12}{5}$; in order
to get access to the corresponding RG beta functions, we derive general
multicomponent beta functionals $\beta_V$ and $\beta_Z$ in the aforementioned
upper critical dimensions, most of which are novel. The field theories we
analyze have $N=2$ (polygons), $N=3$ (Platonic solids) and $N=4$
(hyper-Platonic solids) field components. The main results of this analysis
include a new candidate universality class in three physical dimensions based
on the symmetry group $\mathbb{D}_5$ of the Pentagon. Moreover we find new
Icosahedron fixed points in $d<3$, the fixed points of the $24$-Cell,
multi-critical $O(N)$ and $\phi^n$-Cubic universality classes.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga