The large-$N$ limit of 4d superconformal indices for general BPS charges

Abstract

We study the superconformal index of $\mathcal{N}=1$ quiver theories at large-$N$ for general values of electric charges and angular momenta, using both the Bethe Ansatz formulation and the more recent elliptic extension method. We are particularly interested in the case of unequal angular momenta, $J_1\ne J_2$, which has only been partially considered in the literature. We revisit the previous computation with the Bethe Ansatz formulation with generic angular momenta and extend it to encompass a large class of competing exponential terms. In the process, we also provide a simplified derivation of the original result. We consider the newly-developed elliptic extension method as well; we apply it to the $J_1\ne J_2$ case, finding a good match with the Bethe Ansatz results. We also investigate the relation between the two different approaches, finding in particular that for every saddle of the elliptic action there are corresponding terms in the Bethe Ansatz formula that match it at large-$N$.

47 pages

References in corpus (12)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Supersymmetric multi-charge AdS_5 black holes
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• EFT and the SUSY Index on the 2nd Sheet
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• Superconformal index of low-rank gauge theories via the Bethe Ansatz
• From multi-gravitons to Black holes: The role of complex saddles
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs

Cited by in corpus (3)

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• S-duality in the Cardy-like limit of the superconformal index