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We calculate and study the general superconformal index for the 6d U (N) (2, 0) theory with four chemical potentials, from the indices of gauge theories on CP² x R. Our index agrees with the large N supergravity index on AdS₇ x S⁴ at low energies, and also yields the negative 'Casimir energy' with an N³ scaling which was recently calculated from a QFT on S⁵. Our approach also suggests a systematic study of the (1, 0) superconformal indices.
Kim et al. (Mon,) studied this question.