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arXiv · 1604.03397

Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces

Seyed Morteza Hosseini·Noppadol Mekareeya
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Abstract

In this paper, we calculate the topological free energy for a number of ${\mathcal N} \geq 2$ 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 $S^2 \times S^1$ 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 $\mathrm{SL}(2,\mathbb{Z})$ duality.

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Seyed Morteza Hosseini, Noppadol Mekareeya. 2016-04-12. Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces. https://doi.org/10.1007/jhep08(2016)089

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