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On the superconformal index of Chern-Simons theories and their KK spectrometry. (English) Zbl 1476.83142

Summary: We study the large-\(N\) limit of superconformal index for two strongly interacting Chern-Simons theories in three dimensions with \(\mathcal{N} = 2\) supersymmetry, and compare the result against the AdS/CFT dual, namely the data of full Kaluza-Klein reduction spectra obtained using the exceptional field theory technique. The two theories of interest are mABJM and GJV theories, which are obtained as IR fixed point of RG whose UV description is ABJM and maximally supersymmetric Yang-Mills theory respectively. We confirm agreement and the duality persists. For the case of mABJM it turns out that we need a refinement of the gravity index which reflects the fact that the UV description on the field theory side has enhanced global symmetry.

MSC:

83E15 Kaluza-Klein and other higher-dimensional theories
83E50 Supergravity
58J28 Eta-invariants, Chern-Simons invariants
81T17 Renormalization group methods applied to problems in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
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