Abstract
We consider the superconformal index of three-dimensional \( \mathcal{N} \) = 2 supersymmetric field theories computed via localization on S1 × S2. We systematically develop an expansion where the ratio of the radius of S1 to the radius of S2 is taken very small — a Cardy-like expansion. We emphasize the sub-leading structures in this Cardy-like expansion as well as their interplay with the large-N limit for theories with gauge group of the form product of U(N) factors. We demonstrate that taking the large-N limit first leads to an expression for the effective action yielding the index that only includes terms proportional to 1/β and powers of βi=0,1,2 where β is the ratio of radii. As we depart from the β → 0 limit for finite N, we find indications of non-perturbative contributions of the form e−1/β. We present an explicit evaluation of the superconformal index for the ABJM theory in the large-N limit that is exact in β up to non-perturbative corrections. For the ABJM theory we explore the implications of the Cardy-like expansion for corrections to the entropy of the rotating, electricallly charged, asymptotically AdS4 dual black hole. Interestingly, we find a closed form for the entropy that includes all perturbative corrections in β and takes the form of the leading order expression but with shifted charges.
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Lezcano, A.G., Jerdee, M. & Pando Zayas, L.A. Cardy expansion of 3d superconformal indices and corrections to the dual black hole entropy. J. High Energ. Phys. 2023, 44 (2023). https://doi.org/10.1007/JHEP01(2023)044
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DOI: https://doi.org/10.1007/JHEP01(2023)044