Abstract
The large-N limit of ABJM theory is holographically dual to M-theory on AdS4 × S 7/ℤ k . The 3-sphere partition function has been obtained via localization, and its leading behavior F (0)ABJM ∼ k 1/2 N 3/2 is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading \( \mathcal{O}\left({N}^0\right) \) order by computing the one-loop supergravity free energy as a function of k and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with F (1)SUGRA ∼ k 6, while F (1)ABJM ∼ k 2. This suggests that the low-energy approximation Z M-theory = Z SUGRA breaks down at one-loop order.
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Liu, J.T., Zhao, W. One-loop supergravity on AdS4 × S 7/ℤ k and comparison with ABJM theory. J. High Energ. Phys. 2016, 99 (2016). https://doi.org/10.1007/JHEP11(2016)099
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DOI: https://doi.org/10.1007/JHEP11(2016)099