A gravity interpretation for the complex Euclidean saddles of the ABJM index
Abstract
The superconformal index is a grand-canonical partition function that counts the 1/16-BPS states in the theory, and its Legendre transform with respect to reduced chemical potentials accounts for the Bekenstein-Hawking entropy of electrically charged rotating black holes in anti-de Sitter spacetime. However, the superconformal index of N=4 super Yang-Mills theory appears to allow shifts in chemical potentials, and the contributions of the shifted terms diverge exponentially. This puzzle was resolved by showing the instability of wrapped D3-branes corresponding to the shifts in the gravitational on-shell action. Analogously, we study the ABJM index and the M5-brane instability criterion.
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