All known 3d N=8 and N=6 SCFT moduli spaces are quotients by reflection groups, predicting two new N=8 theories and proving the equivalence of two ABJM theories.
3d superconformal indices and isomorphisms of M2-brane theories
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abstract
We test several expected isomorphisms between the U(N)xU(N) ABJM theory and (SU(N)xSU(N))/Z_N theory including the BLG theory by comparing their superconformal indices. From moduli space analysis, it is expected that this equivalence can hold if and only if the rank N and Chern-Simons level k are coprime. We also calculate the index of the ABJ theory and investigate whether some theories with identical moduli spaces are isomorphic or not.
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hep-th 1years
2019 1verdicts
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Reflection groups and 3d $\mathcal{N}\ge $ 6 SCFTs
All known 3d N=8 and N=6 SCFT moduli spaces are quotients by reflection groups, predicting two new N=8 theories and proving the equivalence of two ABJM theories.