The topologically twisted index of \(\mathcal{N} = 4\mathrm{SU} (N)\) super-Yang-Mills theory and a black hole Farey tail

DOI10.1007/JHEP10(2021)145zbMATH Open1476.81126arXiv2108.02355MaRDI QIDQ825764

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Publication date: 17 December 2021

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Abstract: We investigate the large-$N$ asymptotics of the topologically twisted index of $mathcalN=4$ SU($N$) Super-Yang-Mills (SYM) theory on $T^{2}imes{S}^2$ and provide its holographic interpretation based on the black hole Farey tail. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of $mathcalN=4$ SYM theory as a discrete sum over Bethe vacua, to compute the large-$N$ asymptotics of the twisted index. In a dual $mathcalN=2$ gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-$N$ limit. This extends the previous microstate counting of an AdS${}_5$ black string by the twisted index and thereby improves holographic understanding of the twisted index.

Full work available at URL: https://arxiv.org/abs/2108.02355

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