Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superpotentials for superconformal Chern-Simons theories from
  representation theory   These notes provide a detailed account of the universal structure of
superpotentials defining a large class of superconformal Chern-Simons theories
with matter, many of which appear as the low-energy descriptions of multiple
M2-brane configurations. The amount of superconformal symmetry in the
Chern-Simons-matter theory determines the minimum amount of global symmetry
that the associated quartic superpotential must realise, which in turn
restricts the matter superfield representations. Our analysis clarifies the
necessary representation-theoretic data which guarantees a particular amount of
superconformal symmetry. Thereby we shall recover all the examples of M2-brane
effective field theories that have appeared in the recent literature. The
results are based on a refinement of the unitary representation theory of Lie
algebras to the case when the Lie algebra admits an ad-invariant inner product.
The types of representation singled out by the superconformal symmetry turn out
to be intimately associated with triple systems admitting embedding Lie
(super)algebras and we obtain a number of new results about these triple
systems which might be of independent interest. In particular, we prove that
any metric 3-Lie algebra embeds into a real metric 3-graded Lie superalgebra in
such a way that the 3-bracket is given by a nested Lie bracket.

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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex