Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A one-loop test for construction of 4D N=4 SYM from 2D SYM via fuzzy
  sphere geometry   As a perturbative check of the construction of four-dimensional (4D) ${\cal
N}=4$ supersymmetric Yang-Mills theory (SYM) from mass deformed ${\cal
N}=(8,8)$ SYM on the two-dimensional (2D) lattice, the one-loop effective
action for scalar kinetic terms is computed in ${\cal N}=4$ $U(k)$ SYM on
${\mathbb R}^2 \times$ (fuzzy $S^2$), which is obtained by expanding 2D ${\cal
N}=(8,8)$ $U(N)$ SYM with mass deformation around its fuzzy sphere classical
solution. The radius of the fuzzy sphere is proportional to the inverse of the
mass. We consider two successive limits: (1) decompactify the fuzzy sphere to a
noncommutative (Moyal) plane and (2) turn off the noncommutativity of the Moyal
plane. It is straightforward at the classical level to obtain the ordinary
${\cal N}=4$ SYM on ${\mathbb R}^4$ in the limits, while it is nontrivial at
the quantum level. The one-loop effective action for $SU(k)$ sector of the
gauge group $U(k)$ coincides with that of the ordinary 4D ${\cal N}=4$ SYM in
the above limits. Although "noncommutative anomaly" appears in the overall
$U(1)$ sector of the $U(k)$ gauge group, this can be expected to be a gauge
artifact not affecting gauge invariant observables.

22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs