Large N universality of 4d N=1 superconformal index and AdS black holes

Abstract

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We study the large <jats:italic>N</jats:italic> limit of the matrix models associated with the superconformal indices of four-dimensional <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 1 superconformal field theories. We find that for a large class of <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 1 superconformal gauge theories, the superconformal indices in the large <jats:italic>N</jats:italic> limit of such theories are dominated by the ‘parallelogram’ saddle, providing <jats:italic>O</jats:italic>(<jats:italic>N</jats:italic><jats:sup>2</jats:sup>) free energy for the generic value of chemical potentials. This saddle corresponds to BPS black holes in AdS<jats:sub>5</jats:sub> whenever a holographic dual description is available. Our saddle applies to a large class of gauge theories, including ADE quiver gauge theories, and the theories with rank-2 tensor matters. Our analysis works for most <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 1 superconformal gauge theories that admit a suitable large <jats:italic>N</jats:italic> limit while keeping the flavor symmetry fixed. We also find ‘multi-cut’ saddle points, which correspond to the orbifolded Euclidean black holes in AdS<jats:sub>5</jats:sub>.</jats:p>