Abstract
We study the superconfomal index of four-dimensional toric quiver gauge theories using a Bethe Ansatz approach recently applied by Benini and Milan. Relying on a particular set of solutions to the corresponding Bethe Ansatz equations we evaluate the superconformal index in the large N limit, thus avoiding to take any Cardy-like limit. We present explicit results for theories arising as a stack of N D3 branes at the tip of toric Calabi-Yau cones: the conifold theory, the suspended pinch point gauge theory, the first del Pezzo theory and Yp,q quiver gauge theories. For a suitable choice of the chemical potentials of the theory we find agreement with predictions made for the same theories in the Cardy-like limit. However, for other regions of the domain of chemical potentials the superconformal index is modified and consequently the associated black hole entropy receives corrections. We work out explicitly the simple case of the conifold theory.
Highlights
JHEP03(2020)088 presented in [12, 13]
We focus on the conifold theory in which the simplicity of the superconformal index allows us to study it for some region of the domain of chemical potentials that can provide a black hole entropy with corrections purely depending on the angular velocity τ
We have essentially found that, selecting a set of chemical potentials that ensures an optimal obstruction of cancellations between bosonic and fermionic contributions to the superconformal index, one can always find a region of chemical potentials where the index accounts for the black hole entropy
Summary
Na = N ∀ a, the same numerical value for all nodes In these theories the weight vectors ρ are such that for any bi-fundamental field Φab (notice that in the more generic notation used in [9], the index a of Φa would split into ab): ρΦijab (u) ≡ uaijb ≡ uai − ubj. It is natural to make an attempt with a direct generalization of the type of solution encountered in [8], namely: uaijb (ia − jb) These solutions appeared first in [27] while evaluating the topologically twisted of 4d N = 1 theories on T 2 × S2 in the high temperature limit; it was later shown in [28] that such configuration provides an exact solution to the Bethe Ansatz equations.
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