Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monopoles, three-algebras and ABJM theories with $\N=5,6,8$
  supersymmetry   We extend the hermitian three-algebra formulation of ABJM theory to include
$U(1)$ factors. With attention payed to extra $U(1)$ factors, we refine the
classification of $\N=6$ ABJM theories. We argue that essentially the only
allowed gauge groups are $SU(N)\times SU(N)$, $U(N)\times U(M)$ and
$Sp(N)\times U(1)$ and that we have only one independent Chern-Simons level in
all these cases. Our argument is based on integrality of the $U(1)$
Chern-Simons levels and supersymmetry. A relation between monopole operators
and Wilson lines in Chern-Simons theory suggests certain gauge representations
of the monopole operators. From this we classify cases where we can not expect
enhanced $\N=8$ supersymmetry. We also show that there are two equivalent
formulations of $\N=5$ ABJM theories, based on hermitian three-algebra and
quaternionic three-algebra respectively. We suggest properties of monopoles in
$\N=5$ theories and show how these monopoles may enhance supersymmetry from
$\N=5$ to $\N=6$.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin