Abstract
In this paper, we calculate the topological free energy for a number of \( \mathcal{N} \) ≥ 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 × 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 \( \mathrm{S}\mathrm{L}\left(2,\mathbb{Z}\right) \) duality.
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Hosseini, S.M., Mekareeya, N. Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces. J. High Energ. Phys. 2016, 89 (2016). https://doi.org/10.1007/JHEP08(2016)089
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DOI: https://doi.org/10.1007/JHEP08(2016)089