Abstract
We study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting holomorphic functions on the associated Calabi-Yau cone. This observation allows us to use standard techniques developed in the context of quiver gauge theories to obtain explicit results for a number of examples; namely S 5, T 1,1, Y 7,3, Y 2,1, Y 2,0, and Y 4,0. We find complete agreement with previous results obtained by Qiu and Zabzine using equivariant indices except for the orbifold limits Y p,0 with p > 1.
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Schmude, J. Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone. J. High Energ. Phys. 2015, 119 (2015). https://doi.org/10.1007/JHEP01(2015)119
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DOI: https://doi.org/10.1007/JHEP01(2015)119