Large N superconformal indices for 3d holographic SCFTs

Abstract

We study a limit of the superconformal index of the ABJM theory on S1 × S2 in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the 1/N expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d $$ \mathcal{N} $$ N = 4 SYM coupled to one adjoint and Nf fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in AdS4.

Maximally symmetric nuts in 4d 𝒩 = 2 higher derivative supergravity

“…However, the generic form of other partition functions given in [2] still relies on the full validity of (4.1) combined with the gluing rules for the particular background in question. It is a non-trivial holographic check that both the twisted and the identity gluing rules (see [1,18]) lead to the correct finite N answer for the topologically twisted and superconformal indices of ABJM, respectively, as numerically verified in [61] and [62]. Additionally, at large N , the refined topologically twisted index of ABJM was also shown in [63] to agree with the proposed gluing rules applied to (4.1), generalizing the analytic result of [64].…”

Holographic thermal observables and M2-branes

“…where the coefficients (α, B, C) are the same as the ones appearing in the topologically twisted index (4.4). We note that in [37] this relation between the two different indices was shown analytically for the N = 6 ABJM theory and the 3d N = 4 SYM theory known as ADHM (or the N f model). We have recently improved on this analysis and have shown that this relation is valid for general 3d N = 2 SCFTs [38] and we can therefore employ it safely in our current discussion.…”

“…The superconformal index can be studied in the Cardy-like limit of small ω, which physically corresponds to the limit where the size of the S 1 circle is much smaller than the radius of the S 2 . 7 In this regime, it was shown in [37] that the index takes the form…”

Large N partition functions of the ABJM theory

“…For a number of interesting theories, we have managed to obtain a perturbatively exact analytic answer for their TTI, which we will report on in a forthcoming publication [70]. Moreover, in [71] we will show how similar numerical techniques can also be leveraged to derive analytic answers for the superconformal index of 3d holographic SCFTs.…”