Large \(N\) topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces

DOI10.1007/JHEP08(2016)089zbMATH Open1390.81600arXiv1604.03397MaRDI QIDQ1639061

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Publication date: 12 June 2018

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Abstract: In this paper, we calculate the topological free energy for a number of $mathcalNgeq2$ Yang-Mills-Chern-Simons-matter theories at large $N$ and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the partition function of the theory on $S^{2}imes{S}^1$ with a topological A-twist along $S^2$ and can be reduced to a matrix integral by exploiting the localization technique. The theories of our interest are dual to a variety of Calabi-Yau four-fold singularities, including a product of two asymptotically locally Euclidean singularities and the cone over various well-known homogeneous Sasaki-Einstein seven-manifolds, $N^{0,1,0}$, $V^{5,2}$, and $Q^{1,1,1}$. We check that the large $N$ topological free energy can be matched for theories which are related by dualities, including mirror symmetry and $mathrmSL(2,mathbbZ)$ duality.

Full work available at URL: https://arxiv.org/abs/1604.03397

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